Hahaha...I like that notion. He's going to fight any attempts to smooth over his appearance, of course, but Izumi isn't really a hostile guy so long as he doesn't feel like he's being looked down on. He'd probably find Suzu a bit irritating, but not enough to purposely antagonist or insult her, and free food is free food.
Now, if she asked to practice against him, that would definitely incur his interest, as fighting is his one true first passion. He'd be willing to help her practice and might even give her a few pointers, though he wouldn't hold back on dishing out a few lumps just because she's a girl.
As far as history goes, it might be hard to get Izumi to open up directly about that, though if they share a history class she'd probably be able to notice him answering questions that left the class sitting in stumped silence for a few moments. He's by no means a genius but he knows his facts, and while some people might accuse him of being only into the historical battles, Izumi can rattle off some pretty obscure info. (...though I'd have to look it up first as I personally am NOT a history buff XD)