I have a chipless key for my runner that I had made just to open the door. If you put it in the ignition and turn it, it will just sit there and crank without firing. That doesn't entirely rule out an immobilizer problem however.
According to Alldata, the rear on my 2005 has a total capacity of 3.2qt. It also says that the oil level should be within 5mm of the lower surface of the opening, so if you filled it to that point I would think it's fine.
For any aftermarket part that *might* affect emissions, always refer to the CARB website. Anything you put on should have an E.O. number associated with it. If it doesn't, then there's a decent chance it won't pass smog. From what I can tell the TRD CAI model number pTr03-35090 has EO D425-43...
There's no reason to pull the radiator for the timing belt, just the upper rad support and fan shroud. Also, if it were low on refrigerant it wouldn't be blowing cold at all. I agree with aha2988 to check the cabin air filter, but I imagine it has something to do with the switch itself. If it's...