Saab 97x 2006 8 cylinder and the gas guage and automated mileage display

The fluctuating fuel gauge is probably a bad fuel level sending unit. There are little teeth that swipe a circuit board which then the computer reads the resistance and tells the IPC the fuel level reading which you see. The gas tank will have to be removed to replace this part. Before doing this have a knowledgable mechanic test the circuit so your not just replacing parts. As for the ignition switch it sounds like theres a problem with the ignition lock cylinder. I believe the problems to not be related.

Did this problem start immediately after the jump start?

recalled for gas tank sensor.