Kudos. I hope you find it as fun as I do. There are times I am itching to jump in their games, but refrain. From my experience, the game really grows on youth when it is a youth activity, not an adult led activity. But it is still fun to watch. (And occasionally laugh at their shenanigan's.)
My influence is I sit there and listen to them play. Smile. And when they ask about a rule, generally like falling or jumping, I explain it to them. I have also handed them the books, including some APs. That's it.
Are they collaborative? Yes. More so than adults? I haven't seen it. They play exactly like I have seen all starting players play: they make characters. Anything goes. Until the DM comes up with an idea - and anything doesn't go. My example was specific and truly showed how they play. The DM wanted to run a war torn world and the players would be half-orc military captives that start on a boat. None of the players needed to be something different. They accepted the DM would take them on a ride, and they were willing to board.
As far as bad calls, they accept them so much that even I have a hard time not looking up with a questioning face. They, look at the DM like they do a teacher, because that is what they are exposed to 8 hours a day, 5 days a week. I don't reinforce this as you implied. They do it because I have them read the first few pages of the PHB.