I am installing a new toilet that has a larger base than the original one. The tack strip and carpet fit the old base but not the new one. Can I leave this alone and simply install the new toilet? Do I need to use 2 wax rings to insure a seal? I want to be sure there are no leaks from the ring down to the sub floor into the carpet.

I would not leave carpet under the toilet. Dry fit the toilet first, take sharp utility knife and cut along the base of the bowl cutting all the way through the carpet. Remove toilet. Finish cutting. Remove any tack-strip that is in your way. Toilet has to sit on solid floor. Install was ring and toilet. If you cut the carpet right it will fit exactly around the bottom of the toilet base. I don't even think you have to install new tack-strip.