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I would check the real temperature of the engine with a lazer pyrometer, that way you will know the actual engine temp to see if the coolant temp sensor is telling you the truth. If the coolant temp and engine temp agree and are too low, say around 150-160 degrees, then replace your thermostat so your can get your engine into closed loop. Until your engine goes into closed loop, the fuel trim not be active and its reading will not make any sense. Fuel trim is an adjustment that is made by the PCM to keep the engine fuel control within a tight spec window, so the engine never runs too lean or too rich. Some call this stoichiometric fuel control. The PCM will add or subtract from the millisecond injector 'on time' which adds to or subtracts from, the amount of fuel delivered to the engine.
P0125 indicates that the engine takes too long to warm up to the minimum closed loop operating temperature which is generally around 170 degrees F. This is almost always caused by a "lazy" thermostat that is stuck open or opens too easily. Replace the thermostat with one that is OEM spec, clear the codes and this will solve the P0125 issues. The P1155 is an air fuel ratio sensor heater problem on bank 2 sensor 1 (this is the cylinder bank that is opposite the bank that has the number 1 cylinder) check the resistance of the heater element in the sensor and if out of spec, replace the A/F sensor, however, please verify that you have a good 12 volt signal to the heater circuit at the proper time before you condemn the sensor. An inexpensive OBD-II scanner will help see this. Hope that this helps.
Best to call a Nissan dealership and have them run your VIN (17 digit vehicle identification number) to see if they have extended the warranty for the Fuel Level Sensor. This is because your vehicle is way past the typical emissions warranty of 3yr/50,000 miles. However if this problem is a known pattern failure of this year Xterra, then you may be covered. A vehicle that is approaching 10 model years old will have some components fail. Also, it's not that difficult to replace the sensor, Nissan usually builds in a panel that allows you easy access to the fuel tank sensor.
It is best to go to the manufacturer's technical web site and look under the technical sections for the translations of the hexadecimal values for your specific vehicle. Dodge may charge you for this info, I don't have it, as I would have to pay to log in as well. If your car passed all the monitors, then you are good to go. If your idle air valve is defective and your are sure of that, then by all means, replace it. As for your fuel economy, look at your fuel trim. Is it rich or lean? When you say bad fuel economy, could you be more specific? How many miles on your vehicle? I would check to make sure your timing chain is not too stretched, as retarded timing will kill your mileage BIG TIME! Do a base line timing inspection. It can be done even though your 5.9 has its timing controlled by the computer. Feel free to ask more questions. Dan