Yeah with Vergil you get to play through the game, playing the same missions as Dante. You make a new save game with Vergil, and start from the beginning, and have to power up his moves and Style. He plays very differently, as he has 3 weapons (all the ones he uses against you in the original) which he uses at once, so you switch between them with L2 and R2. He only has the one style however, which involves teleporting around the place, and instead of guns he shoots those pale blue swords. When you clear the game with Vergil, you unlock different costumes for him, like with Dante.
Bloody Palace is like a survival mode where you get put into an arena and have to fight wave after wave of enemies and bosses, and it goes on for ages. It is pretty cool, and you fight a variety of different enemies at the same times, so you have to deal with different scenarios than you do in the main game.
The other things are just minor
