I'm thinking about getting new headers and a new midsection pipe, which would delete all the cats and the resonator. Would I get any sort of engine lights or error codes deleting the cats?

 

Yes - I think so -- But a pro will have to explain it better.

Basically the computer is looking for a difference between the first o1sensor and the second o2sensor.

If these differences do not meet the value set by Mini, it throws a cel.