Some blood is expected, but as always, check with your doctor if it appears to be abnormal, or if you are concerned.
If the blood is in the cath bag, it may be from irritation in the bladder (that balloon bumping around). If it is leaking on the outside of the cath tube, it may be from the urethra sutures.
Yes, the cath staying in is a tool to help the urethra sutures heal.
I would expect that the doctor will do some sort of exam to decide if he feels that the cath can safely be removed. At least for my surgeon, 7 days is the absolute minimum time, which may be extended if there is any sign of problem.
After the cath is removed, you may still see some drops of blood and "debris", which will be the scabbing coming off the suture. For me, it was a couple of months. Again, you will want to discuss that with the doctor, and have some idea of if/when to call for help.