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The correct tire pressure will depend on the driving conditions and the tire and wheel setup. But for a good starting point - the factory recommend tire inflation pressure is on the driver's side door placard and on the inside of the glovebox - indicated to be 30PSI in my 2002 Corolla.
Personally, I like to inflate mine a littler higher between 38-42PSI, depending on the tire - as I drive primarily on highway roads. Some hypermilers run much higher pressures - some cases 50PSI and higher to squeeze every MPG out of their cars, most owners run around 35PSI as a compromise number for good fuel economy and compliant ride in rougher roads.
Trunk lamp - have to trace back the wiring - possible the bulb assembly is bad (broken wiring) - tug on the wires and see if they are still soldered on. If they are, could be the trunk switch (push pin) is damaged or shorted so it is not completing the circuit and letting power get to the lamp assembly.
For this generation of Corolla - you can run up to a 7" wide wheel without much issue. 38mm-45mm offset range recommended. Can run up to a 17"x7" or 18"x7" wheels, though you'll increase the likelyhood of having to rolling the fenders as the tires that fit those wheels tend to have pretty wide treads. The TRD wheel package for the 8th gen was a 16" wheel, most people recommend sticking with a 16" wheel or smaller for most road conditions / best bang for the buck.
I ran a 205/45-16 tire on a 16"x7" wheel with a 38mm offset - no rubbing unless you hit a big pothole. Choice of tires can greatly influence if you need to roll the fenders or not. I had Yokohama tires that rubbed all the time in the 16" wheel, then switched to a Kuhmo tire of the same size. The thread on the Kuhmo tire was 0.2" narrower than the Yokohama - it didn't rub at all. I still ended up rolling the rear fenders as I didn't want to risk any contact when I load down the car. If I ran a 205/45-16 tire on a 16"x7" tire with a 45mm offset (tire moves towards the center of the car - closer to the strut assembly) - probably wouldn't have to roll the fender at all.
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2002 Corolla S, 1.8L 1ZZ-FE VVT-i
2003 Matrix XRS, 1.8L 2ZZ-GE, VVTL-i (RIP)
2009 Matrix XRS, 2.4L 2AZ-FE VVT-i
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