1.) Is TDD applicable to game development? I'm guessing the answer is yes for large projects/teams, but I don't know about small project games like what I've mentioned I've done/am working on.
Yes. It's directly applicable. I'll shamelessly plug my book on the subject:
For art and design, there are emerging equivalents (there was a great presentation about "art unit tests in Maya" at GDC 2012, but I have not links to it). Pairing applies to other disciplines, but also not a lot of documented "good practices".
2.) If it is, what kinds of tests would one run?
Apart from the typical unit tests for code, for decades, developers have found ways to have games "play themselves". Many times innocuous, minor changes to properties or elements in the game (e.g. physics changes, prop placement) can have tremendous, unanticipated influence on gameplay....kind of a "butterfly effect". Having the game play itself across the levels and platforms with as many variations you can and frequently as you can helps. Usually the limitation is size of the server infrastructure a studio can afford to build. I've seen companies with huge investments here (usually MMO devs).
Hope that helps!