Yes it is illegal to use a fir hydrant to wash your car. If the hydrant is already running due to the fire department testing them or due to it just breaking on its own then it would be fine because the water is being wasted anyway. If the person has started this hydrants water to run just for that purpose then you should call the police immediately. that person is wasting water. GO Green.
Yes it is. That is water the city or county is paying, and when others use it the water raises YOUR bill to be compensated. Most important if a fire truck needs that fire hydrant NOW, they have to wait for people to move their car. It's also against the law in any state to park within so many feet of a fire hydrant.
Some jurisdictions do allow people to make use of fire hydrants for certain purposes, but a permit is required. If you're concerned, it would be a good idea to contact the local fire department and ask if it's a legitimate usage.