Does this sentence change meaning if you say 远吗 with 很远吗? I know 很 generally means very, but not always as strict. So would 很 mean "very" in the case this sentence has that change?
I think it does would mean very in such case. However, "far" or "very far" is just a personal judgement, and the speaker's standard may not be the same as the listener. It is difficult to say it is really a change in meaning.
I think it would mean very in this case. The way I understand it is that 很 can only be used in that other way when it's used as a copula. But this sentence already has a verb (离), so it is not needed.
Sentences that have the same structure "Is A far from B?" in English have different answers in Chinese. Sometimes it's 远吗, sometimes 远不远. How can one tell which to use?
Those are the two interchangeable ways of asking a "yes or no" question so it's up to you which you want to use
I wonder if 远 is a verb in this sentence. Like "distar" in Portuguese means to be far (away).
No it isn't. It is still an adjective. In a Chinese sentence you don't always need a verb, given the right conditions.