BGA VCC and VSS shorted after desoldering
Based on your 2 questions :


Question 1 - Is the chip dead, or is there still some hope left for it?
Answer - Hard to say if device was damaged due to the rework process or it was 
not-functioning even before
Question 2 - Is the hot air station a bad choice for this task?
Answer - No, the hot air station is OK, but at any rate...


...you should "mask" the card bottom side, in such a way the bottom heater heats up 
   only the area where the BGA is located (preserving other components nearby); however, 120-130°C is a temperature good enough for the card bottom side

...as per the top side of the board, you should thermally protect/isolate components nearby the BGA device to rework

EDIT : BGA rework implies 2 thermal stresses, and you certainly know how much the thermal stresses are important. Just for this reason, one of the principles on reworking of massive components (specially on massive boards), is to depopulate the host board as much as possible, before going to desoldering and to soldering a new component on it. 
Also, you have to consider that is if you want to recovery the board functionality due to a damaged component by reworking it, you must keep in mind not to damage or thermally stressing the other components on the board. So, in principle, the rework process should be conducted in a way to stress the host board as less as you can.