I think it could also be translated as "Other men don't interest me.". Do you agree?
Se is in the second position here. In the first position is the whole phrase "o další muže". This phrase can§t really be divided, it is just a preposition and an adjective with the main noun.
Without context, distinguishing the meaning can be difficult. And both are accepted here and in the reverse exercise.
Will it have the same meaning if I switch the clauses, i.e: Nezajímám se o dalšÍ muže.
There is only one clause here. But yes you can shuffle the words in the clause/sentence. Here it does not change the meaning too much, just the emphasis.
It looks like další and jiny are pretty much interchangeable. Is there any difference between them? In Polish the equivalent of "další" means "further" so it sounds a bit strange for me here.