Error code P1105.

HO2S sensor after TWC preheating circuit too high. There is an issue with the O2 sensor (heated). Check wiring and check sensor outputs with live scanner.

Did u check all your vacuum hoses for cracks, code is for a vacuum hose leakage from the charge air absolute pressure sensor, check for this at the pipe that comes from the throttle body alone the top of the engine & down to the turbo intercooler hose, vacuum hose that may be cracked is near way the pipe connects to the intercooler hose, good luck.

Oh by the way also check if intercooler hose section near to the exhaust cat if the heat as burned a hole in the hose under the bottom facing the exhaust, note that the heat will at some point burn a hole in that hose, so check if that is the case also, just one more thing that I remember for u to look for, good luck, sorry I am not near by to look at the car for u, good luck.

U are correct in your thinking, yes fuel pump now that u have explained it like that, to check fuel pressure just visit your parts store buy a fuel pressure gauge, then locate fuel injector rail & in the middle of the rain u should see a black screw on cap remove cap & that is the fuel pressure test port, affix gauge pressure hose, & just turn key on, not start just on for now reading should be 38- 40 psi there about, if that checks out then u will now need to drive the vehicle with gauge attached & monitor pressure reading while climbing up in speed if gauge drops low while at high speeds that u have a faulty fuel pump, & u will need to replace it. Good luck post back.