Can an airliner be refueled while the APU is running?
Refueling an airliner with APU running is a perfectly normal procedure and it is done daily all around the world. The APU is located at the tail cone partially to reduce the risk of fire spreading to the fuel tanks, which are normally in the wings and center fuselage.  

Some operators and authorities (not all) restrict starting and/or stopping the APU while fueling.