There are cabs waiting at every resort - usually just outside the main entrance, near where the ME buses drop off. If you walk out there and look, you should have no problem finding several at any given time. And if, for some bizarre reason, there aren't any waiting (I have never seen this but I suppose it is possible), the bell services folks will be happy to call for one.
Yes, there are cabs at Animal Kingdom. They are to the left of the tram stand in the parking lot next to the handicapped parking section.
Yes there are cabs outside of AK...when you say "faster than"...faster than what - the bus? There is a direct bus from AK to DHS, you don't need to transfer park to park (other than at the TTC for MK - bus to ferry.)
