FWIW, I just googled it, and the Cherry Springs Star Party is June 10-13, the Black Forest Star Party is Sept. 10-12, and the woodsman's show is Aug. 6-8. I don't know of any other major events but that doesn't mean there aren't any, ask first. Keep in mind that while those nights are the official nights, I'm sure some come early or stay late just like we do with the jam.
While those crowds are ridiculous (in the thousands), any new moon night is going to draw a fair stargazing crowd (maybe 100 on a weekend). Moonlit nights generally bring only a handful of stargazers, so its less of a problem. And the observing field is across the road from the camping area, with a line of roadside pines separating the two, so interaction is minimal and you just have to show them a little respect, which isn't a big deal.
Assuming a non-event night, fires and lights are permitted in the camping area, but maybe skip the bright lantern. Don't shine the flashlight in that direction. If you drive in after dark, they ask that you turn off your headlights when you get close. The bathrooms are shared between the campground and observing field, so put a red filter on the flashlight for nighttime bathroom trips. This all sounds kind of ridiculous, but once your there its not a big deal at all.