My first guess is that you have loose connections that caused the codes. I don't have the service manual in front of me, but internet says that P0113 is the voltage is to high from the Air Intake Temp sensor, not that the temperature itself is to high. This could be a short to voltage, or on some sensor circuits it could be open circuit that causes it. The P0036 is heater is too slow which could also be wiring.
You need to start with what does the service manual say for the P0113 code for your particular model. Probably not the real problem for the dieing on deceleration.
Without having to reread your build log, what is the quick history of this. Has this been tuned since the swap from lsj to turbo. Did you buy a kit or piece this together by yourself? How did you handle sensor relocation/replacement?
Maybe I'm confused. What problem are you trying to correct.
Unless you're in Antarctica right now, you probably have a shorted wire somewhere. As the IAT sensor 1 is integrated into the MAF, this may or may not affect the MAF readings as well. It should be blending MAF and VE at idle, but whack MAF readings can also keep an engine from running at idle. You need to chase this down before any other diag.When the IAT sensor is cold, the sensor resistance is high.
CONDITIONS FOR SETTING THE DTC
The PCM detects that the IAT sensor 1 parameter is less than -39°C (-38°F) for more than 5 seconds
Unless you're in Antarctica right now, you probably have a shorted wire somewhere. As the IAT sensor 1 is integrated into the MAF, this may or may not affect the MAF readings as well. It should be blending MAF and VE at idle, but whack MAF readings can also keep an engine from running at idle. You need to chase this down before any other diag.