The issue with the rims may be do to a late model or replacement 14 inch rim that does not have the nubs for the 57 cap to hold pressure. If there are disc brakes on the car, this is a common problem. OEM 57 14 inch rims will not clear the calipers. Nubs can be welded on, or the rims replaced with ones made for this application and wheel cover.
Looks like there has been a lot of nice work done to the convertible. Looks like a few things still need to be completed.
Enjoy the journey and ask lots of questions. This site has endless years of experience with these cars. This will save you lots of $$$ and incorrect work.
This car has front disk brakes so you are correct about that. Still needs some things here and there but I’ll get there.