I split Hive 4 - the big one - over the weekend. The brood and young bees are now Hive 3; the queen and flying bees remain where they were. Both splits are extremely strong. I checked them today, and everything is as it ought to be. Hive 3 has several dozen queen cells - more than I like - and not much open brood. That's good; you want lots of young bees, and not much for them to feed, to ensure that the queens get the best possible treatment.
A queenless hive will always produce queen cells as long as it has eggs or newly hatched larvae. Drones are harder. Hives 3 and 4 don't have a drone cell between them, but Hive 4 does have a lot of drones. They'll probably be a bit long in the tooth by the time the queens are ready to mate, but hopefully they'll still be fertile. Hive 5 is better; it has a reasonable amount of hatching drone brood. The adult queen hatches 15 days after the egg is laid, and flies to mate about 5-8 days later, depending on the weather. Drones become fertile about 12-14 days after hatching, so I'd expect mating in about two and a half to three weeks, weather permitting, at which time I should have some reasonably young drones available. That's critical, as bees produce them when they feel like it, not when the beekeeper needs them!
On a more serious note, I just spoke to my daughter in Hackney. She's OK, but they're rioting outside, and she couldn't get to her placement. She's horrified by what's happening; as she says, the damage they're doing will just make things worse.