Hello,
You can take a bath or sponge yourself when you are self catheterizing. Just take care to avoid contact with the tip of catheter and accidental pulling of the catheter.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
Sure you can but not at the same time. Nothing changes when you self cath except you don't have the need to void.
Good luck.