Can we use the Hubble space telescope to view the Moon? Could we see the Apollo mission leftovers?

I believe this is like asking if a telescope can be used as a microscope. The lens is optimized for a deep field of photon input. That means it will take a small amount of light and make it concentrated enough to make it seem bigger with that given lens. If you pointed that at the Moon you’d get a super blurry and statistically irrelevant image that is useless. You can’t determine what your seeing because you’ve overloaded the lens with photons. The Moon shines very bright and gives a lot of photons; galaxies millions to billions of light years away are so much more dimmer to the point of hundreds of orders of magnitude. The Hubble sees deep and doesn’t function seeing close.

So, to answer the second part of your question: the resolution would be so blurry with excess photons that even if we pointed right at a boot print or a piece of leftover machinery we couldn’t confirm it due to the blur.

Try it out!?: Get a telescope and look at something close. The lens is optimized for a certain distance, too far or too close shows the minimal range of the photon concentration the lens can achieve and gives a blurred image.

Edit: I think this is actually incorrect about the Hubble precisely, but I’ll keep it up so you readers are force to be critical thinkers.