1. The TM's for your gen set are in the manuals section of this forum. Should be listed under: Everything you need to work on the MEP-802 and 803 gen set. Or something similar.
2. To test the K-2, you could read the testing procedure for testing the relay, or, take a wire from a known 24 volt source, and go to the positive side of K-2, and touch the terminal. Be warned, the starter will turn over if the relay is good.
3. The canon plug can be a sow. Use slip joint pliers, but do not use earth moving force.
4. look up the K-2 relay for the MEP-003A NSN, and then for the MEP-803A. Compare the NSN's. Mechanically they are the same. But electrically, is the amperage rating the same? I can't remember. But if the NSN is the same, then its possible to use it, but first test the relay. I think you will find it good.
5. Its best to remove the fuel tank cover, (yes, it has ten thousands screws, I know its a PITA) but when the cover is off, you can see where the float switch is located. You can also see if everything in there is OK.
6. Have you tested the K-16?