The disconnected coil in your picture is for the coin lockout mechanism. It makes sure the game returns coins to the player if they try to insert money when the game is turned off. A lot of home-use games disable this mechanism (by cutting the wire) because the plate can buzz loudly when the game is turned on.
The broken bar is part of the coin lockout mechanism. It looks like somebody tried to tape it back together. You don’t really need to concern yourself with the coin lockout. It does not interfere with starting the game or playing it.
Here’s a good tip for you: whenever you see a black cloth-insulated wire on a coil, that’s the return path to neutral. The non-black wires on coils are color-coded so you can find them on the schematic.
15 is the maximum number of credits you can put on Centigrade 37. You can’t add more credits until the replay unit decrements one of those credits.
What happens when you push the red button on the coin door?