The 32mm tires can work on dirt if it's not completely smooth. I ride on hardpack dirt with 28 road tires daily and that's not fun because the tire is completely smooth. It's not scary or anything but it does squirm around a bit. Just be careful about it. That said though, I've lost it with my hybrid that has 42mm tires when I took a turn too aggressively and the bike slid out and fell over. If it really bugs you, check the clearance on the fork and frame and see if you can fit something bigger.

Disc brakes vs rim brakes...either one should be fine. Disc brakes work a better in the rain but that's about it. There are ups and downs for both.