Evening Felix and Jack,
There are better people here when it comes to B&S engine questions so be guided by them. My two cents is that a bit of smoke on start and idle is to be expected on an old girl like this. If it runs strong and doesn't smoke out the neighbours or oil the plug to the point where it won't start or run, rock on!
Hot exhaust, running lean? Be interested to see what others say here. Again, for mine if the machine has power, idles nice and accelerates when asked, I've just.........rocked on!

Magneto timing? From memory there is nothing to adjust??
Yup, 3 in 1, ordinary engine oil, even WD40 at a pinch.
Have you looked in the subscription section for manuals?
More than happy to give bits to fellow Greenies. Back story is that I've parted out a few machines and am regretting the amount of shed space the bits are taking up. You'd be doing me a favour if you took it. I noticed the bonnet was broken in the photos but it looks like a nice neat repair should be do-able.
You won't find a manufacturing date on the frame. The engine date is the only reference here. 1984. If it's the original engine this makes it a fairly late machine. The only number on the frame is stamped across the front axle beam channel. 4 digits and maybe a letter.
Cheers,