Cobra insurance

Hello- I need help deciding what to do as I am getting outpatient surgery September 30th (cyst & endometriosis removal)

I am quitting my current job on July 25th where
-I met my 1500$ deductible
-have about 3500$ left for out-of-pocket max
-Cobra coverage would be about 350$ or so a month

My NEW job starting August 1st has

-1500$ deductible
-$8000 out of pocket max
-About 200$/month

My questions are

1. Can I enroll in my new insurance AND have Cobra?
2. Which option would you do and why?
3. Can my new employer insurance deny me my surgery?
4. Should I do Cobra and just wait for open enrollment and start my new insurance Jan 1?
5. Can you cancel Cobra benefits any time?