re 1) I'd give the virgin queen swarm a week. The virgin queen was fit enough for flying, but will now need a good weather day and drones available in the DCA to get mated. She may fly a couple days for mating, then will fatten up and start laying. So give her a week from when the swarm moved in before looking for eggs. Since eggs are hard to see, wait another 4 days (11-13 since swarm moved in) and look for the easier to see larvae.
Michael Bush has a lot of good info at his site on swarms. Definitely worth a read depending on whether you want to encourage or discourage swarms.
http://www.bushfarms.com/beesswarmcontrol.htm
re 2) If your queen-right hive has plenty of brood frames I would give one frame of brood (ideally a mixture of eggs, larvae, capped workers, and a honey/ bee bread band of stores along the top of the frame. Depending on the strength of the parent hive you may or may not wish to take the nurse bees currently on the frame. Just do try to NOT take the queen from the queen-right hive.
Having brood to raise will be a strong incentive for the bees to remain in the hive rather than perhaps abscond. If the queen doesn't get mated or is lost to a predator the bees can raise an emergency queen from the eggs/larvae.
Michael Bush has a lot of good info at his site on swarms. Definitely worth a read depending on whether you want to encourage or discourage swarms.
http://www.bushfarms.com/beesswarmcontrol.htm
re 2) If your queen-right hive has plenty of brood frames I would give one frame of brood (ideally a mixture of eggs, larvae, capped workers, and a honey/ bee bread band of stores along the top of the frame. Depending on the strength of the parent hive you may or may not wish to take the nurse bees currently on the frame. Just do try to NOT take the queen from the queen-right hive.
Having brood to raise will be a strong incentive for the bees to remain in the hive rather than perhaps abscond. If the queen doesn't get mated or is lost to a predator the bees can raise an emergency queen from the eggs/larvae.