No, it's quite archaic and formal. You would only use it now if you wanted to be dramatic or funny!

No, it's not used in day to day conversation. I don't think I've ever said it, nor do I think I will ever say it to someone. It has an old-fashioned feel to it, it's more formal, more literary. If you watch films from the 40s or 50s you might hear it. There's another very simple reason for why it's not used day to day, the actual meaning itself. It's used to say goodbye to people who you are not going to see again for a very long time, not just to say goodbye. I've only ever used it in writing in phrases such as 'farewell party' or 'bid a fond farewell.' But in speech. No.

No. It's old-fashioned and poetic. It hasn't been used by normal people since the 1800s. It was never common in the U.S.

It's very rare. I have said "So Long! Farewell! Auf Wiedersehen! Goodnight!" as a joke-y way of saying "goodbye." (https://www.youtube.com/watch?v=Qy9_lfjQopU), but I don't usually say farewell on its own.