1. The water pump should be submerged under water before starting the motor. It is a good water pump, but a lousy air pump and lousy at lifting water up to it.
2. The “springy” feel is air pressure inside the gearcase, caused by plunging the drive shaft in like a piston. Loosening the oil level plug will let the air pressure out.
3. As for being the correct drive shaft, that’s a good question. Of course comparing with a known correct one is one way, but an expensive way if you have to buy one. I’d say dump the oil out and use a flashlight to see if you can see the support down in there (#22 in the diagram). It is a curved piece of metal strap, arching upward, and the shaft rests on it. If the support is in there and the impeller pin is not higher than the pump plate, I’d say it just about has to be the wrong shaft.
4. To my knowledge, they never made a pump “kit” for that motor. You had to buy individual parts.
