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As you're probably aware from your searching (thank you for using the search feature!) the P0171 indicates a lean condition on Bank 1 (the bank on the passenger side in US). According to the factory service manual, the possible causes for this code are:
For lean and rich DTCs: - Fuel system
- Excessive fuel pressure.
- Leaking/contaminated fuel injectors.
- Leaking fuel pressure regulator.
- Low fuel pressure or running out of fuel.
- Vapor recovery system.
- Induction system:
- Air leaks after the MAF.
- Vacuum Leaks.
- PCV system.
- Improperly seated engine oil dipstick.
- EGR system:
- Leaking gasket.
- Stuck EGR valve.
- Leaking diaphragm or EVR.
- Base Engine:
- Oil overfill.
- Cam timing.
- Cylinder compression.
- Exhaust leaks before or near the HO2Ss.
Since you are noticing a very hot exhaust manifold on the passenger side, I'd guess the code is accurate (very lean condition on that side). I'd start by checking for vacuum leaks. If you have access to a scan tool that can access the PIDs/CIDs/component parameters, you should check the individual cylinder misfire counts as well. You might have misfires that are not frequent enough to trigger a diagnostic code, but could indicate which cylinder may have a bad fuel injector. You could try moving the injector around, clearing the codes, then seeing if the misfires following the injector. Without such a scan tool, you could try unplugging one injector at a time to see which one doesn't make the engine run any worse, and that cylinder is likely the focus.
-Rod