Secondary O2 does not matter. It is only there to throw a code if the cat is not working correctly ... and I assume you have no cat at all, so thus the code. But that has no effect on how the car runs.
That said, if you do have a cat, and it is throwing that code, then your cat might be physically plugged up, which can really mess-up how the engine runs, so could explain your mpg.
Yes, with no cat your exhaust will stink! That smell is called pollution!

You might also have some leaks in the exhaust system if a lot is getting into the car ... or does everyone in CA cruise around in reverse with the windows down?
Actually, a rich running engine runs cooler, not hotter.
With the CAI and header/exhaust, your engine should be running a bit leaner than stock, unless it has a K-Pro, or the like, and has been tuned for the aftermarket parts.
Define "horrible gas mileage". These cars get bad mpg on short trips IF all the stuff designed to warm the engine up quickly is disabled/bypassed. You have a CAI, so that is one crime against quick warm ups. Throttle body coolant bypass? Hondata/plastic intake manifold gasket? I'm guilty of all of these, myself. Short trips around town it sucks gas (mid to high teens). Drive to Seattle or the coast and it gets the same mpg it got stock, low 30s.
All that said, might be worth taking it in and checking for exhaust leaks and get hooked up to the computer. Could be your primary O2 is messing up, but not throwing a code.