i won't say it is a must, but i think that helps.. usually dialects have irregular grammar rules and a lot of unique nouns. I am not sure if the elders can speak common Japanese (like my grandma, she can't speak standard Japanese).

Yes. I came back where I live in two years ago.I didn't speak the local dialect.my friends said they feel I am a cold-hearted person. but you will learn naturally when you live there :)

No, it is not necessary. You will never need to know how to speak a dialect. People will always understand you properly. It would be very interesting to know the regional differences of Japanese, though. If you go northward, I found people are almost "shy" to speak their dialect to people coming from THE City or speaking standard japanese. A different case would be Kansai region, where it can be useful to know the way the talk: I think it really represents their "provincial manners", as nao said.

No,I think it's not necessary. But..,if you are interested in provincial manners and customs,it might be better.

No.