Someone had written a while ago to Disney and was told that the "heelies" are not allowed because they fit into the same category as skateboards, in-line skates, etc.
Since the wheels are hidden though, it would be pretty hard to enforce.
We did see a couple of kids with them during our last trip. One was well behaved and just sort of scooting around with his family, staying out of people's way. The other was making a nuisance of himself, rolling down inclines, ramps and nearly hitting quite a few people. His parents never said a word to him, but I can't see how they were not aware.
For the other questions, the only resort that has golf carts is FW. Many of the resorts have bikes to rent (training wheels and all). I don't think BC has any to rent except the surry bikes right on the Boardwalk. BWV may rent some at the Community Hall area (sort of near the BW pool)