Your picture is too big to view conveniently.
I find it almost impossible to figure out wiring arrangements from that "photographic" type of picture. A drawing of the connections is easier to understand - post a photo of the drawing.
You haven't identified the components in the picture.
How is the Arduino powered?
Those 9v batteries are a terrible source of power. They can't produce enough power and they run down too quickly.
Assuming everything is working at 5v and that the unnamed IC is a 7805 voltage regulator then it should be OK just to replace the 9v battery with the 12v power supply.
Note that you don't convert a 5v servo to a 12v servo. You "convert" the 12v to 5v so it can power the servo safely.
...R