That loose case screw is VERY concerning. You need to take it out at least, or install it correctly at best. If it manages to find its way into the balance, the movement hits 'incredibly costly to fix'. That busted spring is also special, and I hope you didn't put it back into the movement.
IMO, I wouldn't wear or move that watch very much without a service. Given the obvious FOD, there is no way of knowing how much more damage could be done to this by doing any amount of running.
As far as the dial: it is very clearly a repainted dial. You should love it, as it came from your grandfather, but the dial means it is effectively worth very little money. That said, if it were me and my grandfather's watch, I'd spend the ~$500 or so to get a sympathetic movement service. You could probably find a replacement dial if it bothered you, but it IS the one your grandfather wore it with, so perhaps not.
