fuzzylogician

I was going to write a thoughtful long response, as someone who is active in advocating against gender discrimination in my field. I have a lot to say, both from personal experience and based on a large dataset I've collected along with a committee I'm active on showing bias in almost all aspects of a woman academic's life once she graduates from college. (Before you ask for the data, it's confidential and we're in the process of writing up a paper, so if you're *actually* curious, ask me about it in a few months.) I'm in a field where there are more women undergraduates and about as many graduate students as male students. But fewer women get onto shortlists for academic positions; in fact, even once on a short list, they are still less likely to get hired than a man on the same list; fewer women currently serve as faculty members; fewer women get chosen to present papers at conferences; fewer women have their papers published in peer-reviewed journals; fewer women get invited to contribute to handbook articles, which feature the top scholars in the field giving an overview of their main research topic(s); fewer women are invited speakers at conferences; fewer women get their work funded by government agencies. I could go on.
But this poster thinks that being a woman magically opens all doors for a candidate, from sample size N=1, and not even having a full picture of that particular one. To which all I can say is, Wow. 

Seconding the above suggestions. You should have a frank conversation with your potential advisors about these incidents. You should also talk to current students. All these conversations should happen in person if possible and on the phone/skype otherwise. No one will put down in writing anything that would be incriminating. There are questions about how much this was a part of the culture in the department and how much it still is. There are questions about how the department and university handled the situation and what measures have been put in place as a result. There are questions about the current department atmosphere and about how this scandal has affected current students and recent alums on the job market. Some of this is unknowable if it was recent, and some of it may not affect you as someone who won't be involved with these professors. But there might be a concern if this means that the department could lose funding or collaboration opportunities, or if it's perceived as not having dealt with the situation and/or having affected advising and student progress in a way that could color the field's perception of you. In most cases like these students aren't judged harshly because everyone understands their position in the food chain. But it's worth having the conversations and understanding where things stand. 

Two minutes on google, and this is all I'm going to contribute to this debate at this point. I've been active for about four years now in a study that has collected actual measures from my field, and I can talk about actual real trends and numbers. Everyone else here seems to be talking about their own personal experience and little else, and having done this for several years now, I've learned that engaging in that debate is a waste of time. Find a female colleague near you and have a one-on-one conversation -- meaning as her about her experiences and really listen to the answer. You might learn something. 
http://gender.stanford.edu/news/2014/why-does-john-get-stem-job-rather-jennifer
https://www.nysscpa.org/news/publications/the-trusted-professional/article/woman-who-switched-to-man's-name-on-resume-goes-from-0-to-70-percent-response-rate-060816
https://blogs.scientificamerican.com/unofficial-prognosis/study-shows-gender-bias-in-science-is-real-heres-why-it-matters/
https://www.npr.org/sections/ed/2016/01/25/463846130/why-women-professors-get-lower-ratings

I was going to write a thoughtful long response, as someone who is active in advocating against gender discrimination in my field. I have a lot to say, both from personal experience and based on a large dataset I've collected along with a committee I'm active on showing bias in almost all aspects of a woman academic's life once she graduates from college. (Before you ask for the data, it's confidential and we're in the process of writing up a paper, so if you're *actually* curious, ask me about it in a few months.) I'm in a field where there are more women undergraduates and about as many graduate students as male students. But fewer women get onto shortlists for academic positions; in fact, even once on a short list, they are still less likely to get hired than a man on the same list; fewer women currently serve as faculty members; fewer women get chosen to present papers at conferences; fewer women have their papers published in peer-reviewed journals; fewer women get invited to contribute to handbook articles, which feature the top scholars in the field giving an overview of their main research topic(s); fewer women are invited speakers at conferences; fewer women get their work funded by government agencies. I could go on.
But this poster thinks that being a woman magically opens all doors for a candidate, from sample size N=1, and not even having a full picture of that particular one. To which all I can say is, Wow. 

Two minutes on google, and this is all I'm going to contribute to this debate at this point. I've been active for about four years now in a study that has collected actual measures from my field, and I can talk about actual real trends and numbers. Everyone else here seems to be talking about their own personal experience and little else, and having done this for several years now, I've learned that engaging in that debate is a waste of time. Find a female colleague near you and have a one-on-one conversation -- meaning as her about her experiences and really listen to the answer. You might learn something. 
http://gender.stanford.edu/news/2014/why-does-john-get-stem-job-rather-jennifer
https://www.nysscpa.org/news/publications/the-trusted-professional/article/woman-who-switched-to-man's-name-on-resume-goes-from-0-to-70-percent-response-rate-060816
https://blogs.scientificamerican.com/unofficial-prognosis/study-shows-gender-bias-in-science-is-real-heres-why-it-matters/
https://www.npr.org/sections/ed/2016/01/25/463846130/why-women-professors-get-lower-ratings

I was going to write a thoughtful long response, as someone who is active in advocating against gender discrimination in my field. I have a lot to say, both from personal experience and based on a large dataset I've collected along with a committee I'm active on showing bias in almost all aspects of a woman academic's life once she graduates from college. (Before you ask for the data, it's confidential and we're in the process of writing up a paper, so if you're *actually* curious, ask me about it in a few months.) I'm in a field where there are more women undergraduates and about as many graduate students as male students. But fewer women get onto shortlists for academic positions; in fact, even once on a short list, they are still less likely to get hired than a man on the same list; fewer women currently serve as faculty members; fewer women get chosen to present papers at conferences; fewer women have their papers published in peer-reviewed journals; fewer women get invited to contribute to handbook articles, which feature the top scholars in the field giving an overview of their main research topic(s); fewer women are invited speakers at conferences; fewer women get their work funded by government agencies. I could go on.
But this poster thinks that being a woman magically opens all doors for a candidate, from sample size N=1, and not even having a full picture of that particular one. To which all I can say is, Wow. 

I was going to write a thoughtful long response, as someone who is active in advocating against gender discrimination in my field. I have a lot to say, both from personal experience and based on a large dataset I've collected along with a committee I'm active on showing bias in almost all aspects of a woman academic's life once she graduates from college. (Before you ask for the data, it's confidential and we're in the process of writing up a paper, so if you're *actually* curious, ask me about it in a few months.) I'm in a field where there are more women undergraduates and about as many graduate students as male students. But fewer women get onto shortlists for academic positions; in fact, even once on a short list, they are still less likely to get hired than a man on the same list; fewer women currently serve as faculty members; fewer women get chosen to present papers at conferences; fewer women have their papers published in peer-reviewed journals; fewer women get invited to contribute to handbook articles, which feature the top scholars in the field giving an overview of their main research topic(s); fewer women are invited speakers at conferences; fewer women get their work funded by government agencies. I could go on.
But this poster thinks that being a woman magically opens all doors for a candidate, from sample size N=1, and not even having a full picture of that particular one. To which all I can say is, Wow. 

Two minutes on google, and this is all I'm going to contribute to this debate at this point. I've been active for about four years now in a study that has collected actual measures from my field, and I can talk about actual real trends and numbers. Everyone else here seems to be talking about their own personal experience and little else, and having done this for several years now, I've learned that engaging in that debate is a waste of time. Find a female colleague near you and have a one-on-one conversation -- meaning as her about her experiences and really listen to the answer. You might learn something. 
http://gender.stanford.edu/news/2014/why-does-john-get-stem-job-rather-jennifer
https://www.nysscpa.org/news/publications/the-trusted-professional/article/woman-who-switched-to-man's-name-on-resume-goes-from-0-to-70-percent-response-rate-060816
https://blogs.scientificamerican.com/unofficial-prognosis/study-shows-gender-bias-in-science-is-real-heres-why-it-matters/
https://www.npr.org/sections/ed/2016/01/25/463846130/why-women-professors-get-lower-ratings

Two minutes on google, and this is all I'm going to contribute to this debate at this point. I've been active for about four years now in a study that has collected actual measures from my field, and I can talk about actual real trends and numbers. Everyone else here seems to be talking about their own personal experience and little else, and having done this for several years now, I've learned that engaging in that debate is a waste of time. Find a female colleague near you and have a one-on-one conversation -- meaning as her about her experiences and really listen to the answer. You might learn something. 
http://gender.stanford.edu/news/2014/why-does-john-get-stem-job-rather-jennifer
https://www.nysscpa.org/news/publications/the-trusted-professional/article/woman-who-switched-to-man's-name-on-resume-goes-from-0-to-70-percent-response-rate-060816
https://blogs.scientificamerican.com/unofficial-prognosis/study-shows-gender-bias-in-science-is-real-heres-why-it-matters/
https://www.npr.org/sections/ed/2016/01/25/463846130/why-women-professors-get-lower-ratings

I was going to write a thoughtful long response, as someone who is active in advocating against gender discrimination in my field. I have a lot to say, both from personal experience and based on a large dataset I've collected along with a committee I'm active on showing bias in almost all aspects of a woman academic's life once she graduates from college. (Before you ask for the data, it's confidential and we're in the process of writing up a paper, so if you're *actually* curious, ask me about it in a few months.) I'm in a field where there are more women undergraduates and about as many graduate students as male students. But fewer women get onto shortlists for academic positions; in fact, even once on a short list, they are still less likely to get hired than a man on the same list; fewer women currently serve as faculty members; fewer women get chosen to present papers at conferences; fewer women have their papers published in peer-reviewed journals; fewer women get invited to contribute to handbook articles, which feature the top scholars in the field giving an overview of their main research topic(s); fewer women are invited speakers at conferences; fewer women get their work funded by government agencies. I could go on.
But this poster thinks that being a woman magically opens all doors for a candidate, from sample size N=1, and not even having a full picture of that particular one. To which all I can say is, Wow. 

I routinely tell my students "pay attention now, XXX will be on the exam". I only wish they'd listen. What I find a little off about this is that you didn't give all of your students the same shot at success. You let the two that you randomly ran into milk you for information. If you basically revealed exam questions to them, even if you didn't explicitly say "this is an exam question", that's going a step too far for me. Broadly saying "make sure you study X", though, is fine.

Since the people asking are well-meaning, I find that it's usually best to just be honest: "I don't have anything new to report yet, but I promise to tell you as soon as I do." And if it's appropriate: "I know people mean well when they ask this question, but it's hard for me to handle right now. I promise I'll let everyone know as soon as I do, but for now it'd be great if everyone would just stop asking." They're excited for themselves and not thinking through what it must be like for you, but since the intention is good, explaining the situation might be all you need to do. 

This board is not here to help with homework questions. This is what you have instructors and TAs. In any event posting a question without showing that you've done anything to try and solve it yourself won't buy you too much good will in a forum designed for people who are pursuing advanced degrees and independent thinking/research. 

@Dalmatian Yes, I have had students cry in my office, usually in circumstances not unlike what you're describing. It happens. Not much you can do about an uncontrollable emotion that sweeps over you, so I'm glad to hear that your professor handled it well. 
@Berk Oh, that really doesn't sound healthy for someone in their first semester. I would strongly advise you to look for support elsewhere, be it through moving to another lab/supervisor or by simply finding a mentor who isn't your advisor. It can be an advanced student, a faculty member, maybe someone in a specialized support group (those exist!). But don't just keep going like this for too long, because you'll find it very hard to finish, and I'd personally question whether you should. A PhD is not worth 5 years of suffering. 

From an outside perspective: you had the whole summer to prep, plus the whole fall + half of spring semester, and there is no way you spent the whole time writing. You could have (and perhaps should have) prioritized studying for your exam more. To me, the story you're telling sounds like an excuse. You're always going to have more than one thing on your plate as an academic, and if you can't handle that, you won't succeed in academia. Now, beyond that, there's a question of whether you prepared correctly, which it sounds like you may not have. You say that there were concerns about your ability to recall your readings and express yourself orally, which isn't so much a problem of having time to do the reading but of doing the extra work to digest, integrate, and actually speak about these topics out loud. I don't know if you did that, but that would be something I would think about. Short version: I don't see anything unfair here. 
Now when it comes to the letter, not knowing your program it's a little hard to know what to say. For one, no one outside your program ever needs to know it exists. These "files" students have won't follow you around after you graduate. So I guess the question is what it does program-internally, and that is something you'd know better than us. The good news is you passed! A pass is a pass. A high pass or a low pass are both just the same a pass, meaning you've been approved to move on to the next level in your program. It sounds like your program isn't shy about letting you know what they think, so if they thought you should leave, they would tell you. Nonetheless, I think it's wise to have a frank conversation with your advisor about this question and get their opinion. If they say you could/should stay, you should ask explicitly how to fix whatever was lacking in your exam. But assuming you stay, you will need to put this unpleasant experience behind you. As I said, a pass is a pass. Impress your committee with your next steps, and they will assume that you've taken their advice in the letter to heart and improved. They won't hold older offenses against you if you're doing well later on. And again, the letter is internal (as is the exam for that matter) and doesn't matter to anyone but your program. You'll be successful in academia on independent grounds that have nothing to do with this exam or letter, so all is most definitely not lost, and you still have a path to success directly ahead of you. 

This is extremely unlikely to be an issue. As a general rule, the punishment (if any) will be relative to the offense. So if we're talking about one sentence, as a first offense, that shouldn't lead to anything nearly as drastic as withdrawn papers or degrees. More generally, each university has its own office of academic integrity that investigates these matters. Someone would have to file a complaint about your offense, it would be investigated, and a measure might be taken accordingly. For something small, probably nothing more than a warning, maybe a zero on an assignment, or similar. Your degree will not be affected by something like this. Cases where someone's degree is revoked or papers are withdrawn are very rare and usually involve much larger scale fabrication of data, plagiarism, or similar. I hope you're asking about these things just out of curiosity, but just in case, plagiarism can get you in serious trouble even if it doesn't lead to a degree being revoked. Cite where appropriate. When in doubt, cite even more. 

We can't really know and this varies, but: 
1. Smaller departments might be more concerned with diversity, in which case this might be an issue. On the other hand, they might have a strategy of developing one (or a few) areas of strength, in which case they might recruit students with those particular specialties, who may very well come from a particular subset of schools.
2. Although adcoms may directly compare two applicants, especially when it's suggestive, I think a more common thing that happens is that a student is compared more generally against previous applicants and students who have similar backgrounds. E.g. "School XYZ has consistently produced students who have done well in our program. (Or: Letter Writer XYZ has consistently written letters for students who have done well in our program. Or: students with XYZ prior experience/courses/whatever have consistently done well in our program.) Given this, Student ABC might be a good candidate for our program." 

This is pretty normal, and shouldn't cause any harm to the relationship. It happens all the time and this wouldn't be the first time this POI tried but failed to recruit a student. 
You can write a version of what you did here: it was a hard decision, you really appreciate the POI's time and advice, but eventually you chose XYZ (you can give a quick reason if there is clean one, such as it was more funding, better location, or whatnot, but you don't have to). Say that you hope to see the person again and maybe get a chance to work with them (and/or meet them, if you hadn't before) in the future. That's all you need to say. 
And next time you're going to be in the same place, e.g. for a conference, reach out and ask if they have time to have a coffee with you. 

Since the people asking are well-meaning, I find that it's usually best to just be honest: "I don't have anything new to report yet, but I promise to tell you as soon as I do." And if it's appropriate: "I know people mean well when they ask this question, but it's hard for me to handle right now. I promise I'll let everyone know as soon as I do, but for now it'd be great if everyone would just stop asking." They're excited for themselves and not thinking through what it must be like for you, but since the intention is good, explaining the situation might be all you need to do. 

Since the people asking are well-meaning, I find that it's usually best to just be honest: "I don't have anything new to report yet, but I promise to tell you as soon as I do." And if it's appropriate: "I know people mean well when they ask this question, but it's hard for me to handle right now. I promise I'll let everyone know as soon as I do, but for now it'd be great if everyone would just stop asking." They're excited for themselves and not thinking through what it must be like for you, but since the intention is good, explaining the situation might be all you need to do. 

Since the people asking are well-meaning, I find that it's usually best to just be honest: "I don't have anything new to report yet, but I promise to tell you as soon as I do." And if it's appropriate: "I know people mean well when they ask this question, but it's hard for me to handle right now. I promise I'll let everyone know as soon as I do, but for now it'd be great if everyone would just stop asking." They're excited for themselves and not thinking through what it must be like for you, but since the intention is good, explaining the situation might be all you need to do. 

Seconding everything @jrockford27 said. The lie was totally unnecessary and speaks to the stress you're in more than anything. I personally would choose to move on from this. At this point you don't know your potential advisor well enough to know how to "come clean" to him without causing yourself potential harm. The chance that he'll find out exists but isn't large (it depends on who he might know at the other department). The chance that finding out about your lie will actually cause him to drop you as an advisee seems very small. This topic of conversation is most likely in the past and won't come up again. If it does, at some point in the future, you'll have a better sense of how to handle it once you know your advisor better. If it does, I think the way to put it is precisely as it was described above: an almost instinctive reaction to impostor syndrome and a fear of how you'd be perceived by your new advisor. A moment of weakness that's led you to do some serious thinking about how you perceive yourself as an academic. But again, I really think it's best to move on.  

Yes- I'm planning on doing some solo travel during the summer. I think it just comes down to doing the social things I want and hoping to meet people along the way
I have a few people in mind that I'll reach out to. 
 
I'm feeling better about this. thanks.

You can present an unfinished project, but you need to be comfortable with the level of detail you get into. You may not have a fully fleshed out manuscript-length paper yet, but if you don't even have an analysis of some preliminary pilot data, that may not be enough to present. You also need to be familiar enough with all the steps of the study to answer any questions, and you don't want to be caught off guard by questions about how much you can generalize from your study, or whether you even have enough data/robustness to say much of anything. Short answer: yes, you can do it, but there's also a line of unpreparedness you don't want to cross. Talk to your advisor. 

I am not sure what the point of this post is, but it is inappropriate for a graduate school forum, and as such, I'm going to lock it.