First, your engine was made on 4 November, 1981. If it was the original engine, your mower would have been made about 6 to 12 months later.
When you clean your tank and carburetor, you may need a new intake pipe flange gasket for where it connects to the engine block, but you may find the old one is undamaged. Similarly you may find you need a new diaphragm for the fuel pump, or you may not. It may be best to wait and see whether you need any parts.
I hope you only ran the engine for a few seconds without oil. If so you may not have done any harm, since there would have been oil film still on the bearings and piston rings. However, don't do it again. Engines with aluminium cylinder bores and aluminium connecting rods with no separate big-end bearing, do not take kindly to that sort of thing.
You should expect a few odd clunks from the engine when you pull it over with the starter. There is a bit of a clack from each tappet, for example. I'd have to hear it to comment on whether there is anything inside the engine to worry about, but there probably isn't. I'll leave it to Deejay to comment on the mower parts and the clutch.
FYI, your three smallest sprockets all look as if their best years are behind them, especially the two on the chain closer to the side-plate. It appears you will need to replace both of those, plus their chain.
