Um, what? Either they're moving relative to each other or they're not.
Huh? There weren't any forces on them before. They were both moving inertially.
You do understand that in our expanding universe, all the galaxies, which are moving apart because of the expansion, are moving inertially, feeling zero force, right? The expansion is not a force pushing on the galaxies to move them apart. It just is the galaxies moving apart.
That depends on the spacetime. See below.
According to GR, I am not dropping an apple on my head; I am releasing it and letting it float freely, while the Earth pushes me upward into it. I am the one feeling a force, not the apple, and the force I feel is not "gravity", it's the Earth pushing up on me.
When I say the concept of "potential energy" doesn't apply to the expanding universe, I'm not talking about terminology or labels; I'm talking about physics. I'm saying that the physics that's going on in an expanding universe is not the same as the physics going on when an apple falls. I'm saying that the physics you are trying to apply the the expanding universe is the wrong physics; you are trying to apply the physics that works in a stationary spacetime, where the concept of "potential energy" is meaningful, to a non-stationary spacetime (the expanding universe), where it isn't. The same underlying theory (GR) can be used to describe both, but the specific models used--the specific solutions to the Einstein Field Equation--are different, and have different properties. The solution that applies to the apple falling has "potential energy" as one of its properties; the solution that applies to the expanding universe does not.