Sleepy feeling.

After I have had my orgasm sometimes I feel really tired. Does this happen to other people as well.

Perfectly normal. If you manage to resist the urge to sleep for about 5 - 10 mins you'll be back to normal. Something to do with a hormone released into a man's bloodstream following orgasm (IIRC)
 
"Can't we just snuggle and talk after sex?", she said.

Women have been complaining about it for centuries. It's totally normal. Men are happy to nap after sex.

Tell her how relaxed and comfortable you feel around her. Try and stay awake for a few minutes and don't snore.