1. As I suggested in the other thread where you posted about your problem, please get the wiring diagrams from TIS. That should show you how the diode is used in the applicable circuit. TIS can be a challenge to find what you need, but it is probably there.
2. Almost any silicon diode will work, such as the 1N400x series, as I mentioned before. (The "x" is a number designating the max voltage, in your case, probably need no more than 12 volts. "1" i.e. 1N4001 is a 50 volt diode.
The only problem is deciding which side is the anode and which side is the cathode (+ and -). The wiring diagram should show that.
3. It looks like from your pictures the damage is the connection, NOT the diode, i.e. the connector is melted. Poor connections can cause that. The diode may still be good. Some volt meters have the ability to measure diodes; look for a diode symbol on the face of the meter. Example:
https://www.amazon.com/AstroAI-Digit...62&sr=1-4&th=1 note the diode symbol on the lower right center.
4.Looks like the terminals are simple mini spade, i.e. 1/8" spade terminals. (Most of the spade terminals we use everywhere are 1/4"). Thus, the solution may be just to buy new mini spade terminals, and attach them to the wires; but you have to know the orientation of the diode first.