1) This has taken me awhile to think of... so hard to decide between Queen Bee, Skeletron, or Eye of Cthulhu. Or maybe Eater of Worlds... I give up on deciding.
2) Plantera. The music is amazing, she's a great fight, decently difficult. Favorite boss of all.
3) Duke Fishron, probably. Frustrating first fight, and requires a lot of thought and effort into building an arena. Maybe Wall of Flesh, for the same concept (at least for me anyway).