Tamten is masculine and so is man. The neuter form is "tamto", e.g. tamto dziecko (that child)

yes, it's masculine

yea i thought if it ends in a consonant its masculin?

mężczyzna is one of the few exceptions

Not a native, but I'm pretty sure they say both, depending what they mean. If the apple is close or somewhere further.

If it is in my hand i would say "this apple", if I am pointing to it I might say either (this/that), but if it has been mentioned already in the conversation I would always use either "that" or "it". Example: "What do you think of this apple?" "That apple is tasty" or "It is tasty", but replying with "This apple is tasty" would sound weird to me unless i was pointing to it.

Any of what?

Yes, the subject of the sentence (That man) takes Nominative.