Is it possible for a car's position to be changing and its acceleration to be
zero?

Of course.

Acceleration means speed or direction is CHANGING.

IF you're driving at a constant speed in a straight line, then you're going places and acceleration is zero.

which piece of furniture will have the most inertia and give the furniture movers the most difficulty in moving?  

answer

a 75kg dining table

3. dark matter

empty space could also be a simple vacuum