It's an old car with high mileage that sounds like it's still doing pretty good. If you start chopping it up and driving it like a race car it won't last much longer.

Look, no offence, but if you want power and "zipp", you do not buy a Corolla. It is just not the car for that. Even without a cat, it will not give you satisfactory racing experience 😉 So better not remove that cat: have mercy with the car. I am not a great Toyota specialist, but without a cat, the ECU of my car would switch into limp mode, with DEcreased power output and INcreased fuel consumption. In order to avoid this, along with removing the cat, you will also have to do other modifications - like ECU firmware downgrade to a lower eco-class, or installation of a special chip which would fake the O2 sensor signal, or else. It is not an easy thing to do, and even in the best-case scenario it wont give you any worth-mentioning benefits in terms of power and zipp.

It will harm your performance. Cars mainly na ones need back pressure if you take out the main cat it’ll throw off your oxygen sensors and ruin performance and cause premature engine damage 

You chop it off & weld/clamp in a straight pipe. If you just punch the guts out you're most likely going to get some plugging wherever it gets stuck.

use the search. This was answered many times.