TrustYourGut

As someone who has lived in Tucson my entire life (and attended the U of A for undergrad), these claims do have some merit.
The weather is beautiful for half of the year, and hostile for the other half. Get used to hearing about how "it's a dry heat" as that's how everyone here justifies it; doesn't make it anymore tolerable. In the summer it's common to have lows in the 90s or even 100s, and during the monsoon season (about 6 weeks or so during the summer) we DO have substantial humidity.
We do have culture and diversity, just have to look for it. Most parts of Tucson tend to naturally segregate themselves, so you really have to explore the city to find diversity. 
The public transportation here is a JOKE. Agree with this comment 100%.
Overall, Tucson is a blue city in a red state. Even as a blue city, most of the blue is located in close proximity to the U of A, and the city tends to get gradually redder and redder the further out you get.
The traffic and infrastructure here are ridiculously bad. It takes about an hour to drive from one end of town to the other. There are two major freeways that go through the city, but they aren't the most useful or accessible for all destinations.
Critters do happen. I live pretty far on the outskirts of the city, and we do have our fair share of scorpions, spiders (including tarantulas), and snakes. But we also have really cool wildlife like coyotes, javelinas, and bobcats. If you have a newer house or even if you just maintain a regular cleaning routine, you probably won't see many critters in or near your house.
Hope that helps! If you have any specific questions about the city or the university, feel free to ask me!

I would be as forthcoming as possible and communicate with the programs who do send you invitations. I think any program worth your time can and should be accommodating to medical considerations that are obviously necessary. Personally, I would be as flexible as possible and leave the accommodations up to them (say you're willing to Skype, take an alternate date, etc, whatever is the most convenient for THEM). Some programs might prefer one over the other, but I would think that if they say a Skype interview is acceptable to them, I don't think it will seriously affect your chances.
In the meantime while you're waiting for invitations and preparing for your procedure, you might (this is what I would do, anyway) designate a person you trust (spouse, close friend, parent, etc) to check your email and maybe voicemail once a day while your in surgery and shortly after to check for invitations. Perhaps even work something out so they can respond on your behalf and explain the situation to the admissions committee. If it were me, this would give me peace of mind that interview invitations weren't just sitting around unanswered and it would also help me to focus on my recovery rather than stressing about interviews.

Seconding what fuzzy said. Introductions and conclusion sections are where people generally relate their work to the bigger picture so that's a good place to read in a paper. I'd also be sure to read their research website to see how they explain their interests. If they have written review articles, those might be good to skim. Or, if your field has some database of federal grants, you can look up their grants and read the public summary parts (usually ~1 page) and see how they motivate their research questions.

The right kinds of questions to prep for will have to do with how your research interests fit with the prof's, and how their expertise will benefit you. Along similar lines, they might tell you about some of their ongoing projects or stuff they're trying to get funded now and have a conversation with you about that. The goal is rarely to actually get you to make a research contribution during the interview; that's highly unlikely. Usually it's just about seeing whether you can hold a conversation about your research and understand what others are telling you. And just as much, it's simply about personality fit: can you have a productive conversation? Does it seem like you will fit with the group? Given that, I don't know that reading papers closely is the most useful thing, although some familiarity is useful. It's more about understanding the bigger picture: what does this prof and their group do? what kind of projects/papers do they work on? what kind of questions do they (generally) ask? how does that fit with what you want to do? 

One person asked me where I get inspiration for my research ideas from. It wasn't that tough of a question, but definitely one that I was unprepared for!
I was also asked why I applied to the kinds of programs that I applied for (basic science/very experimental), given my long-term research and career goals, which are very applied in nature. At first glance there is definitely what appears to be a total mismatch between what I eventually want to do and what I would be trained to do in my program. I luckily had a very clear idea in mind of what exactly I wanted my career trajectory to be and what skills I wanted to learn in graduate school, which allowed me to give a decent answer to the question. 

re: @lpulicefarrow's  comment, the final approved version of the tax bill actually maintains graduate students' current status, so our tuition will not be taxed. (Source)
Some good questions to ask would be: 
What is your mentorship style?  What has been the career trajectory of graduates from the program/your past graduate students specifically? What are your authorship policies?  What qualities or experiences make a student successful in the program? In your lab?  What kinds of supports are available in the program/department/university for graduate students wanting to learn how to apply for funding? Any questions about the funding package that you may have, e.g., will you be provided with summer funding Any specific research-related questions about one of their papers you have read Contact information of current graduate students in the lab Some questions that were relevant for me, that may not be for you: 
For my Master's thesis and/or dissertation, will I be able to collect my own data or will I primarily be doing secondary data analysis? (many POIs already  had large longitudinal data sets) Are there opportunities to collaborate with other faculty members and/or graduate students? How about with faculty outside of the program/department?  
Keep in mind that interviews are all about information gathering. You want to get a good feel of the program and what your experience in it will be like just as much as they are wanting to get to know you and your strengths/weaknesses. It is always better to err on the side of caution and ask questions about things you may not even consider to be relevant at this point in time, because down the line you may have several programs to choose from and making the final decision will require you to look at those kinds of details.
Also, if you don't get enough time to ask all the questions you have, don't worry about it. You can always email your POI to set up a phone or Skype call to ask any lingering questions.

This is the time where many schools are sending out interview invitations and a common (un?)fortunate situation is having accidentally double-booked themselves for interviews**. So, I hope you'll indulge some unsolicited advice:
Resist the urge to respond to interview requests immediately! Consider potential conflicts first.
If you get notification via email, that's great, you can take some time to think about your options before sending that RSVP. If you are notified on the phone, then try not to commit to anything immediately (hopefully the caller will be considerate enough to not even ask you to make a decision on the spot). However, I would rehearse a line to ask for more time to decide in case you get that unexpected phone call. It doesn't matter if you are 99% sure you are free on that date, unless you already know the school in question is your top choice, practice saying something like "I am very excited for the opportunity to interview. I just need to double check my calendar." Then ask if how they would like you to confirm (call back? email?) and ask for a deadline.
While waiting for interview invites, you should think about how you feel about each school and get a rough sense of how you would prioritize one over another. It may also help to know when schools typically notify you of an interview invite and also of their typical interview dates. TheGradCafe's "Results Survey" database is a great tool, and so is searching the forums if people in your field post their dates here. 
The point of this advice is that accepting an interview date and then asking to change it later can reflect poorly on you and cause you extra stress. Instead, make sure you are aware of possible conflicts ahead of time. If you get an invite from School A today but know that School B generally sends invites 2 days from now, and that in the past the A and B interview dates have overlapped, then I would wait a couple of days to see if School B responds before committing to any date with School A. If it would be too awkward to simply wait in (email) silence, it's okay to reply to "School A" a day after the invitation and say that you think the proposed date could work but you just need a little bit of time to ensure there are no conflicts. Then you can ask about a deadline (if one was not already imposed).
(** To clarify, this is not meant to "out" anyone already in this situation! Just hoping to help out others).

Phone calls are a good thing, but I definitely wouldn't say it's a guaranteed admission. In my opinion, anything you can do to make yourself stand out and be memorable will help you in the long run. I have sent follow up emails to several program administrators etc along the lines of "Hi, my name is blah blah, thank you for taking the time to talk to me, I have just submitted my application to your program which is one of my top choices, and I look forward to hearing from you soon" something short and sweet like that. I don't know that it made any difference one way or the other, but I've received interview offers from each of those schools I sent an email to.
Hope that helps, good luck!