Why does ATC ask emergency aircraft about fuel on board?
It depends on the type of situation. If the aircraft is unable to land for some reason, we'll want to know the remaining fuel to get an idea of how long the aircraft can realistically stay airborne. For an aircraft coming in for an emergency landing - as you have already guessed - the reason we ask for remaining fuel is because the fire and rescue personel needs this information. We will also ask such an aircraft if they have any dangerous goods onboard, since we need to pass this info on to the fire crew as well.

During an emergency, we have a checklist to follow that reminds us which information we need to obtain, and who needs to know what is going on. For a tower position, it may look something like this:



As you can see, fuel and dangerous goods are grouped together, indicating that they are essentially the same thing - something that may cause fire, explode or otherwise cause danger during evacuation of the aircraft.