You can go to https://selfsolve.apple.com/agreementWarrantyDynamic.do and enter your serial number. It will show your verified purchase and how much time you have left on your AppleCare warranty.
As for Mountain Lion, my understanding is that it will be free for those who purchased new MacBook Pro's after June 6th or so. It will be $20 for others. I'd just wait until it's released and then worry about it.
Hope some of this helps,