Prop shaft install instruction on mercury 90hp 4 stroke. when removing bearing carrier prop shaft lifted and piece fell off end of shaft.

You can leave the shift lever in forward gear as the system is sprung loaded so that if anything goes wrong at sea with the linkage there is always the option of getting home.
just be careful to ensure smooth relocation on the splined shaft into the linkage socket when reassembling. Before fully tightening the casing bolts on reassembly bring the remote back into the neutral position, then see if the prop spins freely without engaging any gears. If happy finally torque up the five casing bolts.

The 4 stroke shaft drives - usually, yes. One at the engine where the drive shaft/prop shaft goes to the rear end - at the engine end. If you can give your year, make and model I can check for sure. All the best.

REMOVE LOCKING TAB, UNBOLT NYLON LOCK NUT...DISCARD!
PROP SHOULD SLIDE OFF OUTPUT SHAFT...IF NOT PROP IS FROZEN.
IF IT A THRU HUB PROP, AND HAS A RUBBER SHOCK ABSORBING DEVICE...YOU CAN'T REALLY HEAT IT..YOU DEFINITELY DO NOT WANT TO BANG ON THE PROP(SHAFT AND BEARING DAMAGE)
SOMETIMES THE PROP HAS TO BE CUT OFF...REQUIRING A NEW PROP!
TIP: IF THIS IS THE CASE:*** ALWAYS COAT PROP SHAFT WITH ANTI-SEIZE COMPOUND WHEN INSTALL A PROP!!!!!

Take The Propeller Off,
Use The Rear Thrust Washer As a Tool Turn It Upside Down And Put It Back On The Prop Shaft The Three Slots Should Match With Bearing Carrier.,Undo Three Bolts On The Carrier In The Back Of Gear Box,
Turn Carrier Counter Clock Wise Until It Is Loose Remove Prop Shaft Complete With Carrier and Reverse Gear

This Can Be a Few Problems!
1- Check The Control Cables Are Set In The Neutral Position Correctly
Check And Try Again -If Not
2-Is The Control Box Moving The Lever Fully To Forward And Reverse Positions- If Yes
3- Remove Gearbox ,Remove Bearing carrier ,Remove Prop Shaft,
In The Front Of Prop Shaft There Should Be A Pin With Three Ball Bearings **(Will Give You The Problem You Are Having If Left Out) The Pin Should Not Be Flattened Or Badlly Worn ,
Replace If Worn
The Shift Cam Located Inside Gear Box Right At The Back Should Not Be Cracked Or Chipped ,You Can See It With A Torch Through The Middle Of Forward Gear ,Replace If Damaged.
Re Assemble And Test.

Most modern outboards had 2 tapped holes in the casting which would let you put a steering wheel puller on that part wit some all thread and push aginst the end of the prop shaft to get that piece off the lower.o

Prop shafts are actually balanced, if the balance weight has fallen off it will keep damaging the bearing, check for a balance weight, it is like a flat piece of metal stuck to the prop, there may be more than one.

Prop shaft. You have to remove the bearing housing cap. reference number 70. Remove the bearing housing. reference number 60. The bearing housing will need to be pulled out buy using a puller. If it was in salt water it can be difficult. Pull the prop shaft and clutch dog assembly.

As long as it will actually go on the shaft, there will be no problems with changing to the other prop.

Check your prop...probably slightly bent and only is noticeable at higher rpms.