I'd say "Ten pan..." should also be allowed. How else would you translate it in the reverse if I said Ten pan sprzata basen. It would be translated as This man is cleaning the pool.
you are right. I think it is one of the things course creators just did not think about.
I would probably use "człowiek" or "pan" more often than "mężczyzna" in this kind of sentence.
I believe "czyści basen" should be correct too. For example imagine he is cleaning the bottom of the pool, you wouldn't use "sprząta" for that.
cleaning and sprzata do NOT mean the same thing, sprzatacz in French means faire le menage dans une chambre ou la cuisine mais pas dans la piscine