I'm not talking of a regular bow or arrow, but of a large, strong, powerful bow. The type that fires a large arrow, for a long distance. Although, I may have exaggerated, though I still doubt that one would be simply unmoved by any arrow that is meant to kill.

And yes, a wall does push back if you push on it.
If I were to walk up to the wall I am currently facing, and put five Newtons of force into it, then there are two real things that could happen. Either, A, the wall collapses or moves under the force, or, B, the wall pushes back with the exact same amount of force to prevent it from moving. That, or the curriculum that the state of Texas teaches is entirely wrong. Or at least my part of the state of Texas.