Usually, tail-chasing stems from boredom. Most dogs have a prey drive, and if they can't fulfill that drive, they start chasing anything that looks small & fluffy - like their own tails. It's not a problem in and of itself, but some dogs can get obsessive-compulsive, and the constant stress on the vertebrae can cause serious problems later on if not addressed. Distracting him with play is a good thing, but you want to be careful not to let him think the tail-chasing is how he induces you into play. Try breaking it up with a couple puppy push-ups before engaging in the play.
The carpet slide thing sounds pretty normal. Dogs like to rub themselves in stinky things, so just be glad that it's inside on your carpet and not a dead field mouse or a pile of poop outside. Yech.
How old is your puppy? I agree he's probably chasing his tail from boredom. Is he getting plenty of mental and physical stimulation? I would do short training sessions every day. And distract him with another game or toy whenever he does it. Play tug! I bet he would love that! Let him run after and catch the tug toy and chew and pull on it. This behavior could become obsessive.
The rubbing his face on the carpet in normal dog behavior.