FAA Medical Form:

18.V No

18.W Yes...but only if it's a misdemeanor. If it's not a misdemeanor (or felony) then maybe you don't have to check yes. If you think an infraction is not considered a misdemeanor in your jurisdiction and prefer to not report this I would talk to an aviation lawyer first, or at the very least google your state criminal code. Infractions are *generally* not misdemeanors but some jurisdictions may blur the lines.

I doubt this will show up on any background check, unless it happened in your county of residence and they have a searchable website which will list such cases if searched by name.

But this would be unlikely to hurt you unless you're interviewing at a major airline next week. Might be better just to disclose it and demonstrate honesty, unless the questions asked on the app (or at the interview) clearly do not cover infractions. This might raise eyebrows if you're over 30, an RJ CA or military O4...they might expect you to know better. Could always explain it was an honest mistake, you weren't aware of the rule at that location.

This is all just my opinion, of course talk to a lawyer before making significant legal decisions.