Does that mean i can start a floor with a off element team to weaken the mobs first>get defeated>use 2nd key and clear the floor with my water team and get all the missions completed?--
It should mean that, yes.
Just remember that in Kamihime, you can't "pass" your turn. You're going to do damage no matter what (unless Give Up works, I'd assume not). So don't overshoot your damage output if that's what you're after.