Actually it is the old queen that goes with a swarm, leaving developing queen larvae and young house bees (workers) in the old hive to start a new colony.
Whilst there is only one queen bee in a regnant (ruling) capacity her replacement will be alive and "waiting in the wings" to take over on her death or departure.
If the hive still has brood (eggs and larvae in the comb) then there is the chance that the worker bees can make a princess cell from one of the worker cells. If there are drones, then the new...
Bees don't form new hives. A hive is an artificial home for bees supplied by a beekeeper so that he can keep his bees in a location that suits him. Once the bees have been put in the hive they will...