The questions I have now are:
- How could this have happened?
Several possibilities. Overload or age seem most likely.
Overload: not likely if you've been using the Q9550 for a long time.
Age: given that you replaced an E5700, I would put this motherboard somewhere around 2007/2008? Right?
Especialliy if you're using it long and hard, the electrolytic capacitors may have aged by now. One of these going bad might have caused the mosfet to fail.
The photo shows signs of the right mosfet getting very hot, to the point it melted the solder and discoloured the metal. This was not a short sharp overload but a lingering one.
Maybe it's even a combo of the power used by the Q9550 and ageing components on the motherboard.
- Can it be fixed, and if yes how?
Yes. If the pcb is in good shape. Heat exposure may have damaged the adhesion of the traces to the base material. Lifting traces by accident then becomes all too easy.
Make sure all solder has melted before you try to lift the component off. If you have to apply force, then not all solder has melted. IMHO the only method of removal with a chance of succes is hot air. You may want to desolder some of the adjoining caps and coils first to prevent heat damage to them and to give you room to work. It looks like they're through hole devices.
- Can I trust my power supply to safely work on another mobo?
If all voltages measure OK, then yes.
P.S.
I just saw a Teapo cap bottom right in your photo, definitely not regarded as quality caps, esp. from that time period. Wonder what the brand of those next to the mosfets is...