browneyedgirl

departments will usually ask admits who turn them down where they end up going, in my experience, and also have a pretty good sense of the schools admits turned down to come there (through conversations, funding negotiations, etc.)  I wouldn't be surprised if that's where they come up with their list of competitor schools.  my program tends to lose admits to the same set of schools every year, but maybe one student each year goes somewhere we might not expect, based on their options.  to that end, the "surprise" school might well say it competes with schools X and Y because student A turned down X and Y to go there, even though that program, broadly speaking, may not be considered "equal" to X and Y.

departments will usually ask admits who turn them down where they end up going, in my experience, and also have a pretty good sense of the schools admits turned down to come there (through conversations, funding negotiations, etc.)  I wouldn't be surprised if that's where they come up with their list of competitor schools.  my program tends to lose admits to the same set of schools every year, but maybe one student each year goes somewhere we might not expect, based on their options.  to that end, the "surprise" school might well say it competes with schools X and Y because student A turned down X and Y to go there, even though that program, broadly speaking, may not be considered "equal" to X and Y.

I agree with the questions suggested by 3221.  one big piece of advice, beyond that, is to try to spread out the question-asking as much as you can.  if you ask everything up front, or in the first two hours of your visit, you'll probably dread every subsequent interaction when someone from that program asks what questions you have.  I couldn't even count the number of times I've asked this of an admit, only to have them say something like, "well... I don't know... I think I asked all of them..."
 
also, try to ask questions of as many people as possible.  you might run into a grad student or professor who is well-meaning but out of the loop on a particular topic, but still offers an (incorrect) answer.
 
 
 
on professors' research, no, definitely not - remember, this is their chance to sell their program.  you're already in! they're not expecting you to talk about their work.  obviously, if someone's work is pretty close to what you want to do, you could discuss it. I like to use the visit weekends to tell new admits about my program, and to get a feel for who they are, both academically and personally.  there are only so many times you can give the "I'm X, studying field Y, undergrad at school Z" talk.
 
on the methodology question, I would say that's a "must-ask" question - if you're at all concerned that the department does one thing and frowns upon people doing anything else, you shouldn't hesitate to ask.  even if they think it's a strange question (which most people at most schools will not think), it's so much better to know that now than when you've already started there.
 
 
yes.  in my experience, odds are good that the person who e-mailed was on the admissions committee and may have been delegated to e-mail students.  it's also possible that the professor thought your work was interesting and wanted to contact you, even though you didn't list them in your application (though, in your case, perhaps this is less likely).

I agree with the questions suggested by 3221.  one big piece of advice, beyond that, is to try to spread out the question-asking as much as you can.  if you ask everything up front, or in the first two hours of your visit, you'll probably dread every subsequent interaction when someone from that program asks what questions you have.  I couldn't even count the number of times I've asked this of an admit, only to have them say something like, "well... I don't know... I think I asked all of them..."
 
also, try to ask questions of as many people as possible.  you might run into a grad student or professor who is well-meaning but out of the loop on a particular topic, but still offers an (incorrect) answer.
 
 
 
on professors' research, no, definitely not - remember, this is their chance to sell their program.  you're already in! they're not expecting you to talk about their work.  obviously, if someone's work is pretty close to what you want to do, you could discuss it. I like to use the visit weekends to tell new admits about my program, and to get a feel for who they are, both academically and personally.  there are only so many times you can give the "I'm X, studying field Y, undergrad at school Z" talk.
 
on the methodology question, I would say that's a "must-ask" question - if you're at all concerned that the department does one thing and frowns upon people doing anything else, you shouldn't hesitate to ask.  even if they think it's a strange question (which most people at most schools will not think), it's so much better to know that now than when you've already started there.
 
 
yes.  in my experience, odds are good that the person who e-mailed was on the admissions committee and may have been delegated to e-mail students.  it's also possible that the professor thought your work was interesting and wanted to contact you, even though you didn't list them in your application (though, in your case, perhaps this is less likely).

I agree with the questions suggested by 3221.  one big piece of advice, beyond that, is to try to spread out the question-asking as much as you can.  if you ask everything up front, or in the first two hours of your visit, you'll probably dread every subsequent interaction when someone from that program asks what questions you have.  I couldn't even count the number of times I've asked this of an admit, only to have them say something like, "well... I don't know... I think I asked all of them..."
 
also, try to ask questions of as many people as possible.  you might run into a grad student or professor who is well-meaning but out of the loop on a particular topic, but still offers an (incorrect) answer.
 
 
 
on professors' research, no, definitely not - remember, this is their chance to sell their program.  you're already in! they're not expecting you to talk about their work.  obviously, if someone's work is pretty close to what you want to do, you could discuss it. I like to use the visit weekends to tell new admits about my program, and to get a feel for who they are, both academically and personally.  there are only so many times you can give the "I'm X, studying field Y, undergrad at school Z" talk.
 
on the methodology question, I would say that's a "must-ask" question - if you're at all concerned that the department does one thing and frowns upon people doing anything else, you shouldn't hesitate to ask.  even if they think it's a strange question (which most people at most schools will not think), it's so much better to know that now than when you've already started there.
 
 
yes.  in my experience, odds are good that the person who e-mailed was on the admissions committee and may have been delegated to e-mail students.  it's also possible that the professor thought your work was interesting and wanted to contact you, even though you didn't list them in your application (though, in your case, perhaps this is less likely).