Is altitude and heading your discretion when you are cleared visual approach?
Visual approach procedures are discussed in AIM 5-4-23. A visual approach is an IFR procedure and you must be on and stay on an IFR flight plan. It authorizes you to proceed visually clear of clouds to the airport. You may make whatever normal maneuvers necessary to safely conduct the approach and landing including descents and turns. Under most conditions, you are responsible for your own terrain clearance and separation. The exception is if you have the airport in sight but not the aircraft you're following. ATC can still clear you for the visual but will retain radar separation responsibility.

Note that a visual approach is different from a "Charted Visual Approach Procedure," which KSAN happens to have for Runway 27. If cleared for the charted visual, then you must fly it as depicted.