Is the white inside the wound an infection, and how long are wet to dry dressings needed? (Photo)

Great question! The area looks quite shallow, so there's not much to pack. I would recommend keeping it moist (with antibiotic ointment) and covering it with a dry dressing (bandaid). The area should heal by itself. The yellow at the base looks like granulation tissue, which is normal healing tissue.

The white that you are seeing is not a sign of infection in this wound.  Those signs would include pain, redness, and/or purulent drainage.  Deeper wounds heal from the bottom of the wound bed towards the surface.  In other words as it heals it will become less deep until it heals completely and is flush with the skin.  Continue to follow your surgeon's advice for the best outcome.

From your photographs, this wound does not show any signs of infection. The white debris will be pushed out as the wound continues to heal. You are dressing seems appropriate, although it may be easier to apply in appointment and Band-Aid if your doctor agrees.