I own a 1236. In trying to thread, I have issues locking the half nut at the proper time. I'm still pitiful at threading, but figured out better timing for engaging the lock nut. I know I need to practice more (lot's more).
Sometimes I'll have to rotate the chuck when changing speeds. Doesn't seem to be as serious a problem as you have though.
The 'wobbly gear' and ill fiting key may need to be addressed. Probably just remove all connected parts of this gear train and inspect, adjust/modify, and reinstall. It may be that the loose fitting gear caused premature wear on other parts, leading to today's condition.
I also own a PM940 mill. It's leaked oil from around the spindle for years now. I don't use it much (or the lathe) so have lived with it. It got the best of me and I finally took the mill apart. Probably a good thing as there was casting sand and other 'gunk' in the case. Having it apart also revealed the oiler for the fine downfeed was not dropping oil on any gears. All bearings arrived yesterday, so hoping to get back together soon.
It is kind od disheartening to have a newer machine need such work, but seems to be what we have to live with and learn about our machines at the price point we deal with.
I seem to remember someone else having issues and it turned out to be a ill-fitting key/oversized keyway.
Good Luck!