How old are you now?
You can say you had arrests when you were a minor, but not as an adult. If the records are sealed, all the better. It's their job to prove you unsuitable, not your job to prove you are.
Next, for youthful offenses, you'll be fine (well, as long as you have no felonies!). Then, they can sometimes be brought into question on suitability. But most likely those records are sealed as they usually are with minors.
If you're adult life is totally clean, you have nothing to fear. If the local issuing authority tries to play any games, the BFPE will indeed still grant you your permit.
I've seen worse go through and I attend all the BFPE hearings as an observer.