Trevanion
Greatest Of All Time
I think those things are called "nutserts" I've never personally had to fit them so I'm of no help there.
Looking at your photos of the pulley, there isn't a key way cut into the pulley so there would be no point in sourcing any key steel for the shaft (EN8 Grade usually) if you have no matching key way cut into the pulley. New 16mm bore 4-step pulleys with a key way can be had for relatively inexpensive prices but finding an exact match for the diameter sizes might be difficult, but anything that's close enough should work fine. Judging by the amount of marring on the keyway on the shaft somebody's just been tightening a grub screw in there to hold the pulley in place.
Looking at your photos of the pulley, there isn't a key way cut into the pulley so there would be no point in sourcing any key steel for the shaft (EN8 Grade usually) if you have no matching key way cut into the pulley. New 16mm bore 4-step pulleys with a key way can be had for relatively inexpensive prices but finding an exact match for the diameter sizes might be difficult, but anything that's close enough should work fine. Judging by the amount of marring on the keyway on the shaft somebody's just been tightening a grub screw in there to hold the pulley in place.