Do I need to descend towards the Minimum Descent Altitude if I have the airport in sight?
No, you do not need to descend all of the way to the MDA if you have the required visibility to continue. In fact, I would recommend against it since it puts you awfully close to the ground while you are maneuvering to align with the runway.  Why do that if you don't have to?

MDA stands for Minimum Descent Altitude, and is just that.  The minimum.

As far as going missed, you would fly the missed approach in the same way because while you may have obstacle clearance where you are now, the missed approach procedure assumes that you fly it the correct way, and in this case you just have some extra padding since you started out higher.