If I book 2 rooms for 1 night, will I get credit for 2 stays with points?
Yes, you should, as long as you have them both under your MR number. I've done it on a few occasions with new employees traveling with me. Pretty sure the kicker is who's paying for the room.
I have experienced my name, my money, for multiple rooms gives me credit for nights and points. As far as STAYS, as you list it in your question, that I'm not sure. Is there a promo you're trying to hit that is using stays versus nights?
Yes, provided you are paying for both rooms and staying in one of the them.