1) Powder and charge - If you are shooting golf balls instead of metal shot, any granulation powder will be OK because the golf balls are so light. If you graduate to metal shot, then Fg or FFg, depending on the diameter of your powder chamber, is appropriate.
2) Patches - Correct, no patches, just loose powder in chamber and ball rolled in on top. Even with metal shot.
3) Range - If you use enough powder to get 500 yards range, the flight of the ball will be unpredictable. It's better to keep the range at 100 yards or less. With metal shot, I would be uncomfortable with range in excess of 100 yards in a Coehorn style (thin walled) mortar. A thick walled siege style mortar should be OK for longer ranges.