NH State law is 10mph on public roads where permitted locally, but many towns "allow" traffic up to 40mph so the atvs don't slow down local traffic.
Berlin allows the speed limit for a section on Rt 110, and it's slow going in town, and parts of Rt 16 allow ATVs as well, but I don't recall the limits on Rt 16 off the top of my head. When in doubt, 10mph.
You can't run at night by default, though Berlin extends the curfew during events like the ATV Festival, but only for those two/three days.