I can't really figure out how to progress. At night the big shades are too strong to beat, and during the day I can only get some minor stat increases. The first day Opal says to talk to people, but there's no one to talk to. Do I just need to buy a bunch of items and use them to get through the big shades?
That is one way to go, yeah. You can also scavenge the school for items.
Another way is to go to the rooftop, get defeated and start witll all your stats (and maybe items). The game is supposed to be completable within one night, and it is intended to use items. Use D4s, they make poison :P (Local joke from my boardgame group)