An object at rest remains at rest, an object in motion remains in motion at a constant velocity unless affected by external forces. So the box will remain at rest since the acceleration is zero
There can be no single isolated force, for every action there must be a force of reaction of ingual magnitude and direction, but in the opposite direction
Both gravity and centrifugal force act on the Moon which causes it get pulled towards Earth (gravity) and get "flung away" so it doesn't hit us (centrifugal force).
