The mite is called a verroa mite (I'm sorry I don't know the spelling). A teacher of mine (Dr.Bowen-Walker) did his dissertation on it. Apparently it's quite rare to find a hive without infestation. There was a wild hive in my parent's chimney; I tried to save it by getting someone to remove and rear the hive but my father destroyed it because they couldn't come at a weekend
The main bee that everyone is aware of is the apis meifera lieneaus (sorry spelling not accurate again probably) which is indeed one of the few species of bee that dies when it stings you. Almost no wasp or bee intentionally stings anyone. There is no control over the sting reflex it is an automatic response to the stimulation of hairs on its arse end.
If you kill a wasp (please do this repeatedly) and don't utterly mutilate it you can hold it up (a sensible person will do this by its wing) and stimulate the hairs (a biro or pencil will do) you will see the sting shoot out then retract- great biology lesson for kids and adults alike!