I was told that the latter one will replace the earlier one, so it will never happen. I have not experimented with it however

If a player is immobile they will not be able to preform a action for a turn. Unless someone remove the immobile effect off them while chaos is still up. Then maybe, depending on chaos.

Chaos replaces immobile from what I can tell. I've been fightning Team 10. (Shika, Ino, Cho) and Shika has used his shadow possion justu, and the Ino come in and chaos, and my people start fighting mine.

that is because ino chases immobile it to chaos.

but if you use shikamaru/fire main for immobile and then tsunade gives a chaos from a crit, i have no idea what will happen.

they will stack, i use fire main and ningendo, if ningendo chases his mysteries target that target will have both effects up and a healer must cleanse each, but the enemy will not attack while immobile is on them so the chaos is wasted.