How do you propose the flight attendants do that?

It's a short flight (6.5 hours or so) and they will probably stay up for the duration, fooling with the inflight entertainment system and absorbing the adventure, which is sure as heck what I did crossing the Atlantic at their age. More power to them. Tell your daughter to watch for the sunrise as they fly across the Irish Sea. Jet lag? Oh yes. It'll be mighty. They will probably crash hard the afternoon of arrival day, by which time they will have been up for more than 24 hours. You can advise them to try to stay on their feet until 1000pm local time no matter what on arrival day, which is the best way to beat jet lag, but in point of fact they'll do what they want. Which is kind of the point of them traveling on their own.

As registered UMs they'll be escorted through Immigration, but they'd be in the same line anyway and kept together. There is no TSA-style screening or search on arrival, so no need to worry about being "chosen for additional screening." They line up to get their passports stamped, then they go get their bags off the carousel, then they march through the green / nothing-to-declare lane and out into the wide world. Presumably they are being met and not taking the Tube into the city on their own or anything like that. I believe usual practice is for a Virgin rep to keep custody of the kids until they are handed over to a previously named party in the arrivals hall.

The friend with two passports should just make sure to use the same one on returning to the US she did entering the UK, and not mix them up, but she probably knows that.