1. I would not go into a hive and extract a frame of brood below 65-70. You run the risk of killing all the brood in the hive, if it is exposed for very long. Even then you will need some way to keep it warm until you get it into the trap and have bees covering the brood. Put the frame in the floorboard of your vehicle and run your heater is one way to keep it warm during travel.
2. I would not transport nurse bees with the frame of brood. If you are going to take nurse bees to a trap, you might as well make a split of your hive and forget the trapping. You only need the brood to draw out nurse bees, housekeepers, fanners, cleaners, etc., into your trap from the feral colony.
3. Leave it until you are finished, or, until you get enough bees to start a new colony. If it is a large colony you may need multiple boxes to hold all the bees, unless you take them away as the box fills. I like to take them away, start new colonies. If you do not want more colonies you can recombine them later.