I tarp or cowboy camp with both of my kids – a son and a daughter. My daughter started camping this way at 11 without any issues. My son started later (but only because he was older when I went to a tarp) but hasn't had any issues either.
I use a 9' x 12' silnylon tarp for any 2 of us. And bring a 5' x 8' silnylon tarp for me if all 3 of us go.
I made individual bug nets for us. I started with 2 yards of mosquito netting, folded in in half, trimmed it down 1 side so it was just wide enough to pull over the top of me while I'm in a sleeping bag, and trimmed it at the open end (opposite of the fold) so that it was just long enough to cover my arms when out of the bag and folded (covers my chest). I sewed the sides shut, sewed a hem along the open end to take a drawstring, and added a drawstring and cord lock on one side.
To use it, I sit up in my bag, pull it over my head and bag, and lay back down. Then I simply push the material away from my face – it's stiff enough to stay that way with only the occasional repositioning during the night.
My son and I use the bug nets but my daughter just uses a lenght of mosquito netting – about 1.5 yards and arranges so that it's over her head and drapes down, covering her arms without folding them. (I offered sew up a net for her but she prefers to do this.)
We use the bug nets throughout the summer, including in July in the Sierras next to lakes that were turning into meadows (lots of mosquitoes) and have slept undisturbed (except for the buzzing).
We've camped with the tarp(s) from late spring to early fall and have encountered light to heavy rain (sometimes for the better part of the trip) and no one has complained about "only" having tarp to get out of the weather in camp.
Good luck.