Is it a Massey-Ferguson loader..?? You may find the pump and drive coupler looking up the loader model number.
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As far as that driveshaft, a video would be nice to see what part is spinning, and what isn't. From the looks of things in the pics, looks to be a 2 piece drive shaft, like it may be adjustable for different length for different mounts/applications. Most older equipment the mating pieces were splined, but newer pieces may have a single piece of key stock, with possibly a set screw to hold it in place. I'm just taking a wild guess at that. Could be a woodruff key with a slot in the solid shaft back towards the engine, and a keyway in the front tubular shaft so it can be adjusted for length, yet the woodruff key will stay in place.
In either case you should be able to remove pump and mounting bracket and pull the pump off, with the tubular piece coming with it. Might not pull off real easy if a key has sheared and gaulded itself a bit.
If in fact it is a key sheared, that is a built in safety feature/weakest link in the driveline to prevent catastrophic failure. Merley speculation using the SWAG system from what I'm seeing in the pictures. Again, if it is a Massey loader, look that model number up on the AGCO site, it should show everything, and how those two pieces are connected.
