If the engine on 50hp outboard is getting very hot and no water comes out of back of engine does this mean it needs a new water pump kit?

Hello, sounds like you may need a new impeller. This is the small round rubber part with fins that spins( like a water wheel) and helps pump water through the motor. The part is fairly cheap, the labor to install it would vary. It would be better if you could get a manual for the motor and do it yourself.