Deixa is imperative conjugated for "tu".
Deixe is imperative conjugated for "você".
The English language has a saying "Let him be" which means "Don't bother him" or something like that. Could this sentence be translated to "Let the boy be" in that sense, or 1) does that not appear in Portuguese or 2) would it require another word instead of "ficar". Thanks!
"Ser" would be a better choice in this case. "Ficar" has a literal sense of staying at a place.
Anyway, "Deixe o menino ser" sounds incomplete. You could say "Deixe o menino ser o que ele quiser" (as in a profession choice).
For "Don't bother him", you should choose that specific verb: Não o incomode.