Jopo,
For me the catheter discussion always boils down to:
If there is much bleeding at TURBT, you go home with a catheter in and come back tomorrow morning to have it removed. Then, if you can urinate normally, you get to go home without a new catheter.
I have "clogged up with clots" after a TURBT and being sent home with a catheter in, and had to make an emergency return to have the clots "pumped out" (not a lot of fun, but better than clogged). Finally, I understood why the darned catheter.
And, No, you are not (normally) supposed to remove it yourself. Look up FOLEY Catheter to see how it gets locked in place. You could damage something removing it.
Best,
Jack