I spoke to a boy before the Cicus at Waukeens Pomenade and he asked me to look for his mum inside. I finished the Circus, spoke to the spider/mum and told her that the boy is waiting for her outside. I also spoke to the guard and got my reward, but the boy is still there and still bothering me. What have I missed?

I bought the three boys in Umar Hill their Ale and swords, but the Quest is still in my journal. What have I missed?

Re the first quest, I spoke to the mother and she went and got the boy, that was that.
Re the second one, exactly the same as you, I bought the boys swords only, (hey too old to drink but old enough to die, he he). Their quest remained on my books too. Even after speaking to the parents repeatedly.

SPOILER (well, not that big anyways)
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Okay..... the Circus. You need to go into the tent again and talk to the mother again. I talked to her when she was a spider. She's still inside (to the left of the exit I think). Go inside and talk to her, problem solved.

The boys (regardless of what you gave them) is in the cave (at the bottom of the "stairs" up the mountain to Valygar's cabin). Go back there, find them and voila! (If you gave them a sword, you'll have to save them. If they're drunk, I can't remember if you get xp or not. But the quest disappears).

Been to that cave several times, but no sign of the kiddos. Did they go an get themselves killed before I could get there?

Same problem here. I only bought them ale and I've been back to the cave but found bumpkis.

It's time triggered, they only appear at the cave after a while. Is bumpkis a word?