Moon Knight has the following inspiration on his ID card:

Can use Empower when indoors. Can use Enhancement when outdoors

Assume Moon Knight is placed outdoors when called in, but the figure who calls him in his indoors.

1: What power does the indoors figure get? Enhancement because MK is outdoors, or Empower because the summoner is indoors?

2: Assume the summoning figure is a peanut base or larger and is in both an indoors square and an outdoors square. Moon Knight is placed outdoors. What powers can this character access? Would the specific squares of the multibased character access different powers?

It doesn't matter where moon knight is when he's called in. The adjacent fig would gain the inspiration effect regardless. If it's a peanut and both are in outdoors/indoors, it's occupying both.

What he said. The entire effect applies to the adjacent figure, so they'd be able to use whichever power was relevant when it matters.

Cooooooool.