Skip addition lower unit work until you figure out how to get the motor running. Return to it when ready to run. (You will need to at least pressure test to see if and where the l.u. is leaking.)
Buy a new fuel pump (cheap one is fine as mentioned above — square pump will bolt up). Borrow a known good tank and hose/bulb. Get some fresh 2-cycle oil if you don’t have it (TCW-3 rated), and fresh gas. Mix 5.5 oz. oil in each gallon of gas (24:1 ratio).
Put the prop on and test in a 32 gal trash can. Water level should be about half way up the leg of the motor, and a steady spray of water should come out of the port on the back of the leg. Keep the hose running, and don’t operate above a fast idle. Make sure the motor shifts into gear at a low idle without stalling. You really need a working thermostat to tune and run the motor.
You can come close to correct high speed mix in the test barrel without high revving. Try 3/4 open for initial setting.