Had a small electrical fire and have some questions

Went to use my air compressor like I have countless times before, and where the compressor plugs into the extension cord it caught on fire after a few minutes of the compressor running. I've never had this happen before, so I have a few questions.

I know I need to replace the cord on the compressor (one of the male plugs melted, as did the ground). Is there something I should test on the plug to make sure this won't happen again? Like continuity between the two male parts of the plug and ground?

The extension cord: should I just toss it, and just replace the female end (where the fire was)

Nothing seemed odd until it caught on fire. The outlet where the extension cord plugged into is still operating, and the device plugged into the other outlet is fine.