Sir or Madam
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The lower has a u-joint on it with a gasket, that is what usually goes out and causes an air lock in the system, which causes no water to be sucked into the water pump.
Most guys put a thru hull in the boat, this will cause that problem never to happen again. Look at the picture the circled part is the gasket
Now as for the vibration, that can be coming from the universal shaft
As for the prop not spinning fast, you will need to check the lower unit fluid for chucks of metal and color. You could have a complete mess on your hands or maybe somebody took this unit apart and did not put it back together
The shaft is actually on the upper unit off the drive
CLICK HERE FOR PARTS
You need to remove the cover, number 13 in the circle picture in the first reply
I can not post up the manuals due to copy rights, but i do have a link that has the manual i found on the internet
CLICK HERE FOR MANUAL
You will need to do a bunch of things, also a vibration can be coming from a damaged prop or prop shaft and not just a universal joint