Y'all is an informal thing. But I don't think it's distinctly Southern. I have friends from Midwest who use it as well.
As for the plural of "you," I think it may depend on context. Would need to verify though.
I can imagine someone saying, "I would like to invite you all to dinner," or, "I would like to invite you to dinner," covering, in both instances the plural form of the word with the latter being the most grammatically correct (and formal) the former, would sit a bit less comfortable with puritans.
So, in short. You are correct in your conclusions.