Answering the easy part first, that metal-covered-both-sides head gasket can normally be re-used safely, provided it doesn't show any signs of coming part and has never leaked, especially through the middle layer between the metal layers.
Another easy one: the diaphragm from the carburetor is long, long past its use-by date and needs to be dropped into the skip with a long pair of tongs, so you won't get nastiness on your fingers.
The crankshaft extension (called the Power Take-Off, or PTO) is fairly severely damaged at the keyway. To become a good crankshaft it would have to have the keyway milled out wider then you'd have to make a stepped key, to fit both it and the clutch that slides onto it. This is not worth doing except to a hobbyist-machinist with a milling machine and time on his hands. Generally, the most economical way to repair that mower is to get a second-hand engine of the same model, and just keep a few spare parts from the original engine.
The saddest part of the story is the clutch that mounts on the PTO. Over time the captive cotter has run loose, that condition was neglected, and now the crankshaft, engine-side clutch half, and key are all destroyed from the clutch rattling and shaking on the PTO for a period of years. By some miracle the mower's frame rails do not look cracked (they are usually cracked on SB45s with loose clutches, apparently due to the vibration). Most likely the thrust bearing in the center of the clutch will have been damaged: the key had probably slid along the keyway until it hit the thrust bearing.
So, the simplest way to address your situation is to procure a second-hand engine, a new key, a new engine side clutch half, and probably a new thrust bearing but this awaits confirmation when you dismantle the clutch. You will also need to check the clutch generally, and the self-aligning ballrace at the sprocket end of the clutch shaft.
