certainly, deer move in the rain, don't let it keep you in, invest in good rain gear
as far as your stand move, too hard to tell if you messed the deer path/trail, putting scent down, can they see it readily from the path/trail...a bit loaded question here
stick to it, certain you will do fine, and no, i don't think it is unethical to shoot a deer in the rain, if i am confident with my equipment, know it is an ethical shot, i am not worried about it...you need to ask yourself this question and answer it truthfully