1. That chest is the chest which containing the dragon chalice, which you needed for the high hall quest to free lord orabas. You can either use arben's sword to exchange it with the slayer which give you saul quest in the slayer camp, or kill him and the entire camp of slayers to get the key. He will drop the key as loot when die
2. If you are referring to the locked chest outside the champion commander room, the key is at the area where the weapon/ armor smith is at. Try check around the corners and you will notice it.