2. What is the best way to tell which programs are strong in which specializations- the professors' interests/publications, graduate students' areas of interest, some master list?
3. When figuring out which programs are good fits for me, how closely are my areas of interest supposed to align with the professors' intersts? For example, do I look for professors whose areas fall into my period of interest, or genre, or both, or do I look for a professor that fits my particular interests even more specifically than period/genre? And how many professors in the program should match up with my interests to ensure a good fit?
Hmmm, no idea about the first question. Would also like to know that one.
My assumption is that the best way to tell who's strong in what is to focus more on the professors' interests/publications, though students' interests may be helpful--after all, they're being guided by a professor. But definitely consider the professors more--you're going to wind up working with them and they'll guide your own research moderately to tightly (this was my experience, in an English masters program). Agreement/alignment is important!
Also, I'd get as specific as possible--something I didn't do, coming out of undergrad. Grad programs really want to know that you have a definite direction in your research (or can at least look like you're capable of having one, sometime in the future). Period/genre is probably enough correlation for now, but maybe try to have some idea what you would like to look at within this period/genre. In my case, my undergrad 'well, I think I kind of like contemporary literature and sci-fi, but also I like Romantic-Victorian and everything else too, did I miss something?' later became 'I want to study modernism'--then it became 'global modernism'--and then finally, 'global modernist apocalypse/the sublime.' It may not have been as nice and natural a progression as it sounds, but I'm hoping it works better for me this time around than my first.
Lastly, I wouldn't really worry about scouting for many professors who share your interests. Probably two is good. Maybe three or four. Again, I'm not exactly an expert on this whole PhD applications business, but during my masters I wound up working really closely with only two professors and for the most part, my thesis advisor was THE source for research inspiration/sanity/advice. I can't really imagine working a lot with more than just a small group of people, even for the dissertation. It's not at all like English undergrad, where a student typically talks to/works with half of-to-nearly everybody.
Anyway, I hope this helps! Good luck!