Yes, there are a fleet of GC Buses that transport to all the sites, and cover all the parking lot even in town. There other tour groups in town.
There are free shuttle buses that will drive you to various interest points along the south rim
Yes
They have free shuttle busses but I'm not sure they offer tours
Yes, free shuttle near visitor center
Theresa is a network of "local buses" to move you they different interest places
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