Building code info is available here:
https://codes.iccsafe.org/codes/new-york
It'll take some work to dig up the specifics you asked for since they're a bit encyclopedic. Might just want to call the Town Assessor to get a simple answer.
Different people have widely varying sensitivities to noise and children's games. My old neighbor built a fence because the 5 yr old kids next door kept lobbing balls into their yard. After she put the fence up, the balls just got stuck in her back yard so she'd scream at the poor kids. Finally she got bit by a brown recluse, and that calmed her down for a while.
You could discuss with your neighbors first if there's a concern; often that step will alleviate issues down the road.