have there ever been any cases of tanning beds causing sterility?  Is
the skin on the scrotum sac and penis thinner than on the rest of the
body?  Is it more ceceptable to skin cancer?  Or, can the testicles be
affected more easily because of how thin the skin is there?

I think a researcher gave up on this question, but I think that I can
safely say that there is no problem. You probably won't even get a
sunburn, at least not more serious than one anywhere else. And the UV
stops with the skin, so what's underneath won't be affected  (or the
manufacturers would have long since posted big warnings, and
reproduction in prehistoric times would have died out.  I doubt that
that is what led to the demise of the Neanderthals, but it sure did
not for our predecessors.)
And, if a researcher had found anything bearing on the subject, he or
she would probably have posted it.