Sprocket cover removed, doing inspections

Was looking for sprocket and chain wear and to check for oil leaks.  This chain and sprocket have been on the bike since I've owned it (1987) and could be the original, not sure.  Does the picture of the teeth indicate wear to the trained eye?  And I've attached a movie showing the nut that holds the sprocket on is loose enough that I can turn it.  Only the locking tab is preventing it from turning all the way off.  I'm assuming this nut should have been much tighter than it was.

I also have some play on the shift shaft.  A little bit in and out and slightly side to side.  Is there a tolerance on what's acceptable?  And if not are there easily accessible replacement parts.

And lastly on the part where the clutch cable attaches there is some sloppiness in that assembly.  Hopefully the movie shows that.
 

Nothing abnormal in what you describe.
Shift shaft movement sounds normal without the outer cover fitted.
Sprockets can loosen over time which is why the lock tab is there to reduce the risk of it going awol and causing a disaster.
Sprocket teeth have began to hook due to wear so worth fitting a new one along with the rear and drive chain .