Does “Good morning, esteemed/respected professors” sound like a natural/appropriate opening for a self-introduction in an interview for a postgraduate program?

I think it depends on where you are as not all English speaking places are that culturally similar. In the US, I would say this is a little too formal.

Definitely don't use that form when directly addressing a group, it's typically considered overly formal and in the worst case indicates some sycophancy. Honorifics like that are usually reserved for third person conversation, something like: "Dr Monroe, my esteemed colleague, has written a new book"

I don’t think it would be harmful, but I would say it’s overly formal.

I wouldn't say it's formal so much as obsequious. We don't address people like that. You could say "good morning professors" if you want

“Honoured” is a little more usual in this instance. If the situation is formal, then calling people out be name is the most respect, followed by honourifics. So maybe “Good morning Vice Chancellor Smith, Dean Brown, honoured professors, ladies and gentlemen” might be the right approach. That would be very formal and more appropriate for giving a speech at a ceremony. For an interview situation, I would just go with “Good morning professors, my name is John …”

For English native speakers, using the title - Doctor / Professor etc. - is formal and respectful enough. “Good morning, professors.” (Formal) “Good morning, my name is Iluvfruitnmilk, …” is neutral register. It probably would be OK.

No. Just “Good morning” is enough.

Are you sure they're all professors? That's a specific title / rank and not just a word for an academic scholar. Would be like addressing a group of military people all "Good morning Lieutenants".

No, it sounds snarky and sarcastic because it is so grandiloquent (excessively florid and antiquated). Nobody has spoken like that since the 17th century, so expressions like that are roughly 400 years out of date.

It sounds rather pretentious. KISS, keep it stupidly simple.

I would absolutely go for the simple “Good morning, my name is…” More than that could easily come across as sycophantic.

As in, speaking? No. It sounds pompous or ironic. Neither seems like the tone you would want, unless you are already familiar with them. In writing it *might* be ok.