In the campaign you have to defeat every other player-char, you don't need to defeat NPC-compagnions. When I played with my friend, I did not need to defeat my NPC-compagnion, only his player char and his compagnion.

You can teleport down to the chests to loot them, but you need to loot the corpse of the NPCs in the second round, otherwise they just disappear.

Warrior habe skills on their own with AoE like battle stomp, whirlwind, etc?

The winner of the Arena of the title "The One" can get his collar removed. (Magister won't like that tough.)