Does a herniated disk cause excruciating stabbing pain intermittently as well as a constant burning?

Potentially: A herniated disc surely can cause pain and the pain can be sporadic or continuous. It will often cause pain along the distribution if a specific nerve going into the leg.

Yes, it can: The discs between our vertebrae have nerve endings on them, and when they get injured, those nerves themselves cause constant low level pain. Also, if the disc herniates, it can push against one of the larger nerves going into your buttock and leg and cause intermittent shooting pain.