I would bring 2 circuits on a 3-wire, as it sounds a bit much with the AC unit.
Otherwise, the answers IMPO are maybe to #1, and maybe on #2. (See 250.32) FYI a 3-wire is still a single circuit if it has a handle-tie on the OCP. Either way the #2 answer depends on if there are parralel metallic paths to the shack and the building the circuit comes from.
250.34 Portable and Vehicle-Mounted Generators.
(A) Portable Generators. The frame of a portable generator shall not be required to be grounded and shall be permitted to serve as the grounding electrode for a system supplied by the generator under the following conditions:
(1) The generator supplies only equipment mounted on the generator, cord-and-plug-connected equipment through receptacles mounted on the generator, or both, and
(2) The non–current-carrying metal parts of equipment and the equipment grounding conductor terminals of the receptacles are bonded to the generator frame.
Portable describes equipment that is easily carried by personnel from one location to another. Mobile describes equipment, such as vehicle-mounted generators, that is capable of being moved, on wheels or rollers.
The frame of a portable generator is not required to be connected to earth (ground rod, water pipe, etc.) if the generator has receptacles mounted on the generator panel and the receptacles have equipment grounding terminals bonded to the generator frame.