[DaleHCook]

I really don't know what kind of material the cord is made of, it seems to be the original one.

David addressed the spring, and the use of rosin. The best rosin is that intended for musical instrument strings - if you have any musical instrument dealers, check with them. Online, the best flux is also sold by musical instrument dealers. You want something in solid form, which is generally preferred to paste or liquid. As for the cord, the manual does not specify what was used. The 1942 Philco parts catalog offered a thinner black cord, and a thicker white cord, but their diameters are not specified.

Why do my knobs fit so loosely? Are they incorrect for this model?

Knobs are generally held in place with one or two set screws, or with a flat spring which goes between the knob and a flat on the shaft. AFAIK, 1942 Philco knobs all used set screws. A good photo/photos of the knobs, and a description of their material, will help us to determine if they are the original knobs.