Only in a “well technically” sense. Moon weighs far too much for a mere nuke to do much to its orbit or mass, and any debris you kicked up with one would be lost among all the other bits of grit too small and common to bother enumerating.
2.4km/s. Anything not launched at escape velocity will return. Objects at orbital velocities will return to the impact site after a single orbit (more or less, this isn't counting the effects of earth's gravitational pull).
But wouldn’t it take a while? I’m imagining a dust cloud of epic proportions. But I guess without an atmosphere, the only effect would be gravity, so it would all have to settle back down somewhat quickly?
I’m imagining a sci-fi plot where you have two competing moon bases. And as one group is leaving, they detonate a bomb which kicks up enough debris to incapacitate the other base.
The Moon's Hill sphere is just under 52000 km in radius. This is the distance at which the Earth's gravitational influence is greater than that of the Moon. Using Keplerian orbital mechanics (i.e. KSP-style patched conics) as an approximation, a circular orbit at that distance takes about two weeks. This is the longest possible orbit around the moon (approximately), and therefore an upper bound on the maximum amount of time it can take for something to shoot up from the moon and fall back again.
EDIT: A couple of things to note: in the absence of other bodies, my argument wouldn't apply, as the Hill sphere would be infinite. I'm assuming here, for simplicity, that anything that exits the Hill sphere doesn't fall back. This is not entirely accurate. It's possible that something might enter orbit around the Earth, and hit the moon at some point in the future, but I'm ignoring that.
