"Would you not like an Irish tune played by someone who is not Irish ?"

If its done well, yes. In Poland there are several groups playing Celtic music and doing it extremely well. If I didn't know they were Polish I wouldn't know any better. However, it might be different if they are singing. One group plays celtic music and the singer has very poor spoken English (pronuciation, diction etc) and when he sings a song it is unintelligble a lot of the time. He should stick to his instruments.

"Would you enjoy an Irish Song if sung by an American with an American accent or even just a couple of words that has wrong pronunciation?"

Not a problem, as it is arguably part of the historic process of migration and diaspora. A couple of hundred years ago the original singer may have pronounced things differently too.

"Do you enjoy American Country Music sung with a false accent ?"

Depends how false. The British Rockabilly band Matchbox used to do some songs about Dixie and the accent was laughable. There better stuff was when they didn't.

"Should American Fiddle music only be played on a fiddle?"

No.

"Do you enjoy a Opera singer singing Folk Music?"

No, for similar reasons mentioned by others.

"Should a Copper Song be only enjoyed if sung with a Sussex accent?"

I'll hazard a 'no' here but I've never heard one to judge against.

"Should music of other countries only be performed or recorded by musicians from those countries?"

Depends. Some songs are openly played and shared across cultural and geographic borders. However, the player should understand the context of the song and whether it is appropriate to sing/play it. If a book of Yiddish songs is available in a shop then me playinmg the tunes shouldn't be a problem. However, getting a CD of sacred ritual tunes and playing them in a drunken session would be highly inappropriate.