Would it be wrong to say 'bachgen mae e'?
Yes, but the reasons involve discussing subjects, predicates and all manner of grammatical nonsense that you probably don't want to know.
(If you do want to know, Google "welsh identification sentences")
Brian, I think the correct sentence would be 'bachgen ydy o'?
Is there a difference between "e" for he in this sentence and "o" for he?
"e" is more southern, "o" more northern, I believe. No meaning difference.
Does the word bachgen sound like bachlor to anyone?
Bachgen? Tri deg pedwar oed dw i!