If velocity is zero, then acceleration must be zero too. Acceleration is the same as velocity. The acceleration of a falling object depends upon its mass. Freely falling bodies can only move downward. There is no gravity in a vacuum.
Gravity only acts on things when they are falling.
All objects can be moved with equal ease in the absence of gravity. All objects eventually stop moving when the force is removed. Inertia is the force that keeps objects in motion. If two objects are both at rest, they have the same amount of inertia. Velocity is absolute and not dependent on the frame of reference.