What you've described is called a false awakening (FA). It's basically a dream, only you dream that you've "awakened" from sleep. They're fairly common with WILDs. The best thing to do as soon as you feel that you've awakened is to try a reality check (RC). If it fails, you should become lucid and that heavy feeling should dissipate.

The experience you had with floating around your room was a lucid dream, or at least what one might be like. Technically, if you didn't actually know that you were dreaming at the time (which is what it sounds like) then it's not a LD. Some might call it an OBE, but I'm really partial to that line of thought. The best thing to do if that ever happens again is a RC, then you should be lucid and can bend the rules ad infinitum.

Here's a link to some good LD threads.

http://dreamviews.com/community/showthread.php?t=23857
http://www.dreamviews.com/community/...ad.php?t=38954