Catalytic Converter in or out?

Hi guys, so I have a 93-94 ae101 levin, Currently my exhaust has in like two middle resonators and still the Catalytic converter in it. My O2 sensor is currently not in, but I want to cut out the Catalytic converter because I was told that the car would go alot faster If i did. But is it true that it will burn alot richer and waste more gas since I dont have in the Oxygen sensor? Also, my exhaust is smashed down and squeezed a bit near the sub frame from when we dropped the gear box for a service. The car works really well, I was wondering if this squeeze gave the car some back pressure that it needed, or shud I fix it? and take out the Catalytic converter as well? So many questions got me rambling a bit, hope some one can understand and help me still.

I read somewhere that the performance gains from removing a cat is like 1HP tops.

... here it is:
http://www.importtuner.com/features/0610impp_catalytic_converter_removal/index1.html

if you have a single catalytic converter placed after the o2 sensor in the exhasut system then removing the catalytic converter will not be a bad thing. However running with an o2 sensor is going to ruin your fuel aconomy as if the ecu doen't detect it it just takes a wild guess at how lean it can run safely and over richens the mixture just in case. squashing the exhaust down pipe (i'm guessing that the bit that had the gearbox dropped on it) isn't the end of the world provided the overall size of the hole (was a diamter when it was round, guessing its kind of semic sricle now) the exhaust gas has to flow through hasn't changed to much.
back pressure is not an actual 'thing' its used by many people to over simplify what actually makes an exhaust system flow better. The key in N/A exhaust is to maintain exhuast gas velocity (hence a larger diameter pipe slows the gasses down to much, in part due to laminar flow, in part due to lack of momentum and other factors).

THanks for the replies guys.