Yeah, I always have both of your problems. For the first, I try to breath through my nose and that seems to help out a lot. If your nose is a little stuffed then keep nasal spray by your bedside.
As for your other question, I find that doing nothing and taking it all in when you first become aware is the best way of remaining calm. I do this, gather all of my thoughts and then do what I set out to do. Rubbing your hand and/or spinning does help stabilize dreams so I really dont know why it awoke you. But do what I mentioned above and you will see that your dreams will last a little bit longer than they are.