Neither of those means an immortal person - 不死 means immortal (and is an adjective using の "no" before the noun it describes)
To say "immortal man" I guess you'd use 不死の男? (or 人 instead of 男 to mean "person" rather than "man".)
Uh, and it'd be nice if you stuck to one topic, there's no point asking the same question several times.
Edit: I will also graciously accept the possibility that I'm wrong. If I am, someone please correct me.
