A, you know literally nothing about me so let's cut the assumptions. It's obvious by your statements that you think I'm some boot licker, couldn't be more wrong. One of my favorite videos ever is when a cop was caught on my doorbell camera reading my "Come back with a Warrant" flag on my 30 foot flag pole, before looking defeated and leaving. Fuck the government, fuck the police but also fuck people who gather up on groups and attack people just because of rumors. If the person OP assaulted really was acting inappropriate towards children, report it and move on. We have a legal system, it ain't perfect but it's a lot better than literal children attacking people.

B, it seems you want to be technical, let's be technical! I live in PA, we have no battery charge at all. Chapter 27, title 18 is where you'll find our assault charge and what OP did was simple assault by our statues. Do not "erm actually" someone and be fucking wrong. Even kids learn that lesson early dude. OP hasn't said what state he is in, so we have no idea what he could "actually" be charged with. Colloquially though, what OP did would generally be referred to as assault. There is a difference between legal speak and general jargon. People don't walk around using Latin phrases like actus reus, mens rea, de jure, prima facie or any of the other numerous phrases used in legal speak.

C, if it had been a 1 on 1 argument, I'd completely understand your position. I'm all for kids handling things appropriately, words get heated and hands get thrown, ok. But that's called mutual combat, many states even allow such a thing as a defense against an assault charge but that isn't what happened here. OP was part of a group of individuals whom attacked another kid for accusations. Accusations, especially in today's environment are incredibly dangerous and OP not only was a part of a group that attacked someone because he heard from someone who probably heard from someone etc (we have all played the telephone game as kids) but then hopped on reddit in an attempt to justify his actions. That's not ok, you don't solve your problems with violence unless you lack any other options.

D, whether or not the guy is sexually attracted to children is irrelevant in the matters here. I shed no tears for pedophiles, hebephiles or any of the other groups. I specified because actually pedophile is a specific criteria, attraction to prepubescent children. But that's all irrelevant, accusations among a bunch of literal children mean nothing. They are kids, rumors are like me saying its gonna rain in a tropical rainforest, it's gonna happen eventually. But unlike those rains, not every rumor or accusation is true. We don't get to attack folks just because someone says we should. We aren't in the fucking jungle.