[Mysterious Driver]

Ok well the other night magically out of nowhere i started my car up leaving a friends shop and at Idle my car started leaning out to the point were the wideband stops reading. While cruising the wideband reads normal at 14-15 but when going into boost at wide open throttle it leans out to 13.2-13.5 it's really weird it feels like it may be a fuel issue cause at idle it almost feels like the car wants to shut off and viberate all very little. NOW prior 2 days before this issue i noticed when starting the car up it takes a little longer then it's suppose to before it turns on like if the battery was weak.

The next day I replaced the Fuel Filter with a brand new 300zx TT with my old one that i been running for 2 years without changing it thinking maybe it's a fuel issue and there's a clog somewhere. when the engine sits cold the wideband reads normal then starts leaning out all the way after driving again. I checked my adjustable FPR and it reads normal like it's supposed too, anyone have any idea what could it be? Bad o2 sensor, Bad fuel pump, a blown exhaust or turbo gasket???

Please help thanks!