Can the colossi be beaten in any order?
Do the colossi need to be beat in the order they are introduced to you in the game, or can they be beaten in any order?
No.
They must be killed in order, you cannot sequence break.
No. there are bridges to several areas that the colossi are in but the bridges arent formed until you defeat the colossi that appear in the area before the one you are trying to. the ones you can get to without a bridge simply dont show up.