P0420 Error: Unauthorized Catalytic Converter or Oxygen Sensor

I've been having problems with my 2001 Prism (110,000 miles) and hope you will be able to offer some advice. I got a P0420 error in Februrary and took it into the repair shop to be diagnosed. They diagnosed a catalytic converter was faulty. I ended up getting the converter replaced at a local muffler shop and received the P0420 error again a month later. All this time, the car ran fine but with slightly less fuel milage performance. Theorizing that it was an oxygen sensor, I replaced the front oxygen sensor. The car immediately started acting up within a couple minutes of startup acting like it wasn't getting enough fuel and after a minute of that, would run fine. Frustrated, I took it back to a mechanic and they diagnosed it again. They are telling me that the new oxygen sensor is bad and detecting that the engine is running too rich and thus starving it of fuel when it is cold. They also say that the catalytic converter is not a manufacturer's original part and thus needs to be replaced. When the old sensor was put back in, the car again runs fine.

Questions:
1) Can a catalytic converter that is not original cause the p0420 error code?
2) If the old oxygen sensor with the unauthorized catalytic converter allowed the car to run fine, but with the error code, why does the new sensor cause it to run poorly with no code?
3) Is there a way to disable the oxygen sensors so that I don't have to replace the catalytic converter yet again? Reprogram the Engine Control Module somehow?
4) Is it possible to buy a bad new oxygen sensor and could I return it (to the local NAPA store) with receipt or do I need to offer proof of voltage reading to show that it is bad?

1. yes an aftermarket cat can cause that code, if not efficent enough. a cat and o2 sensor should be changed at the same time. cats really only go bad with oil or a too rich condition for a long time. did you do a 90 k service? have the plugs been changed. computer doesn't read the o2 sensor until it goes into closed loop so if it happens when the car starts, you may have another problem. u can unplug the 02 sensors but the car will only run the base/wot fuel map it won't adjust to rich or lean conditions and the cel will be on. you may be able to return the o2 just get it on a scanner and the check the voltage output. most likely you will need a new cat because that may have been contaminated because you didn't change the o2 or have a recent tune up.
drew

I bought the car at 100K and had a full service done at that time. I also put new plugs on the car at that time. The non-OEM catalytic converter was installed earlier this summer and probably only has 1000 miles on it, all but maybe 30 miles of that was run with the original oxygen sensor (which I presume was bad all along) and thus running on the default settings. Thus I assume the non-OEM catalytic converter is still almost brand new and good, just not sufficient enough for a new front oxygen sensor.

that front o2 sensor should help the cat work more efficiencly, not hinder performance, possible bad o2 sensor i guess from the factory, check to see if your car is cali emissions also, may be different o2 sensor or even air fuel sensor

gm cars can be persnickity about the cats you feed them the money spent on oem is not wasted.
new parts are not always good .
upstream o2s set fuel trim dowm stream o2s monitor the cat. a lazy sensor there can be a problem.
it can be seen graphed on live data stream. if up and down mimick each other the cat used all nine lives. but a marginal part can be tricky to dianiose. scan tools are only as good the person at the helm.
yes you can trick them.