Yeah Kate is a adorable and I'm definitely in the protect her at all costs club XD
As for who you can date, for the main routes it's Kate, Violet, Damien, Matt and Nathan. Nathans takes a while to date him though, as you say you're kind of just friends atm and Nathans not one to jump into things. Matt is an asshole and I'm not sure I'd even call it dating but he is one of the main options. Damien is the other guy you can get with, you meet him if you stand up for him when he's being bullied in the hallway on your first week.