Yes, you can use any engine you want, or no engine at all. Some people even go so far as to write their own “engine” prior to the challenge, but I’d personally call that cheating… 😛
Yep! Whatever engine you want! I’m using RogueSharp, which isn’t so much an engine as a library with some common roguelike algorithms, such as room generation, pathfinding, and that sort of thing.