How correct is the Southern colloquialism "y'all" in correct English grammar?
Solution 1:
Yes. "Y'all" is a contraction for "you all", and so you have placed the apostrophe correctly to account for the missing letters. (You will frequently see the incorrect form "ya'll", but this doesn't expand correctly.)
Also be aware that "y'all" is always plural. Never use "y'all" to refer to a single person! You wouldn't use "you guys" or "all of you" to refer to one person, so don't use "y'all" either.
Solution 2:
Y'all be is never grammatically correct