How many queen bees live in a hive?
Long term, there can only ever be one queen in a hive.
In the process of preparing to swarm, the queen will lay eggs in special queen cells. She will then leave with about half of the worker bees. The remaining workers will look after the developing queen larvae, feeding them with royal jelly as well as pollen mixed with honey, up to the point where the larvae pupate. The workers then cap the cells with wax.
The first adult queen to emerge from the brood cell will then search out all other queen cells and will sting them to kill the other developing queens. A queen bee's stinger is not barbed, so she can withdraw it after use.
If two queen happen to emerge at the same time, they will fight until one manages to sting the other to death.
The only natural exception to the 'one queen' rule can be where a failing queen (i.e. losing the ability to lay fertile eggs) co-exists for a while with her daughter. But that co-existence is only temporary and short term - eventually the old queen dies or is ejected by the bees, leaving the new queen to reign. This is quite a rare situation.