Is studing opening literature on current games ...

I'm new, and didn't see anything about this. I'm not terribly familiar with most openings, so if an opponent goes down an unfamiliar line, am I permitted to reference information on that opening?

Yes! From the "Terms of Service":

(b) While a game is in progress you may not refer to chess engines, chess computers or be assisted by a third party. Endgame tablebases may not be consulted during play but you may reference books, databases consisting of previously played games between human players, and other pre-existing research materials.