"Which country would you choose to live in?"
To say 在 would be less idiomatic and, I'm not 100% sure, but not "standard" Chinese（标准华语/华文/中文）.
That's right, it'd be asking the listener to choose where they'd like to stay instead of where they'd e.g. prefer to or as a hypothetical question.
The question does not contain a word for 去。so I don't think the answer needs 去。
why do you need 会? Wouldn't that change the meaning to "what country will you choose to live in?"