I purchased the Starter Set and unexpectedly the neighborhood kids wanted to try it. We had kids of ages 7, 8, 10, 11, and 12. We played in two sessions. Session 1 handled the ambush and ended with starting to track the last goblin. Session 2 explored about half of the Cragmaw Hideout.
The kids had a great time. They were full of creativity and often would state their conjecture (even wildly off-base guesses as to the plot).
In running I often had to deal with them speaking over one another. Sometimes it was okay, just suggestions. Other times it was contrary or unrelated to what the other kid was saying. I generally let them do this for a bit, then focused everyone on listening to the current person. If I had heard something worthwhile in the interruption I might say something like, "your team members had other ideas, do you want to solicit their help or go with your current plan?" Overall, this was minor and just something to keep under control.
A couple of times the kids considered lawless behavior. They realized they could steal the wagon, for example. Here we paused to talk about their characters and what they believed in. Bonds and other Inspiration-related rules helped to reign them in, especially when I pointed out how Inspiration could grant Advantage on a roll. I also created a personal relationship between the dwarven cleric and their employer, making it more likely they wanted to both stay true to the mission with the caravan and help them when they learn their fate.
The kids did not have issues with the rules. Rather than go over their character sheet up front, I would play and then show them how to do something when it was relevant. I copied the character sheets so I had a reference and could look up their info and help them. "See this big rectangle here?", I would say pointing, "that's your skills. You always roll d20 and add or subtract this number next to the skill name."
Spells are tricky. It took a while for them to understand the difference between cantrips, spell lists, memorized spells, and spell slots. Here it might be better to review this with spell casters up front. Quickly summarize each spell, have them circle the spells they want to have memorized today, and remind them that for 1st level spells they get two castings. I would have the older kid look up her spell info, but for the younger ones I would look it up for them just to save time. For the next session I'm going to make a cheat sheet... it wastes time to look spells up.
Kids are creative. I tried to say "yes" or "yes, and" when possible so the game was fun and reacting to them. If they want to set a trap for the goblins, sure, make a skill check and how well it plays out is driven by that role. Want to try to convince the wolves to help? Sure, but it takes a really good roll or great ideas on how to achieve that.
I had a lot of fun and look forward to another session this week. Two of the kids are mine, and they were both really excited by the game. Nice to see a whole neighborhood of kids speaking positively about D&D - and all of them but one are younger than I was when I first played D&D!
