what a cool looking mill. Sounds like you're stocking up a really neat workshop!
For the rear spindle nut, I would personally make a keyed steel lock washer (you may even be able to buy one), polish it on the bronze bearing side and mill a matching key through the threads on the spindle. Slide it on and then use the nut (personally I'd make it out of steel) to take up the slack in the bearing. A suitably sized belleville washer (I think that's what they're called) between the lock washer and a double nut is another option as this will allow some movement when the machine heats up from use, but maintain the correct bearing preload. Either way, oil from the oiler should keep any friction to a minimum, although you could always grind a couple of oil ways in the washer to make sure.
The first option is sort of how my ancient mini lathe works. Very occasionally I have to slacken it off a touch if the garage is hot and I do a lot of work with it, but most of the time it stays as it is. I tighten it to the point where the chuck stops after 1/2 a rotation or so. I would avoid any kind of compressible washer as the spindle will move when it cuts, leading to chatter and other kinds of mess.
As for the stuck flat head screws, use an impact screwdriver. One of the ones that you hold in your hand and smack the end with a mallet. The impact drives the driver into the screw, so it doesn't slip out, and also provides the shock needed to break the threads loose. I had to use mine to take apart the cross slide on my lathe and it worked a treat, came loose with one tap after several different nerve wracking attempts using a normal screwdriver.