1. Third button -- check the wiring harness, starting at the edge connector (where the board plugs in) and see if there are wires coming from pin 24 (Parts Side) and pin b (Solder Side) -- these pins are 5 in from the end of the connector (see below). They may or may not be labeled on the connector, but they will be on the far end from the black, red, orange and yellow wires at pins 1-6. Pin 7 is a "key", which is hopefully indicated by a white piece of plastic inside the connector itself.
If there are wires there, then trace them as they likely aren't connected to anything. Connect those wires to the "NO" connector on the button switch (24 is for Player 1; b is for Player 2) and connect the "COM" connectors to the ground (pins 27,28,e,f ... or the "COM" connector on an adjacent button).

2. Not always possible, but where it is ...
HobbyROMS -- Steph is the man!