Development of the bees

How much time to the bees need until they are born:This depends if it is a queen, worker bee or male.
The queen takes 16 days, a worker bee 21 and a drone 24 days.
The size of the honeycomb cells are prepared by the worker bees. If it is a normal sized cell, the queen puts in an egg and fertilizes it with semen which is stored in her bladder. In case, the cell is larger, it is meant for a drone, she puts in a non fertilized egg. 

Have a look at this picture. The white stuff in the open cell is a larva, not closed yet, the closed cells are further in their development and just above the larva you see a bee which is just being born and coming out with her head first.