Your Singer is very nearly the same as my 50's Singer. I have a knee pedal but I don't have the door just a tip out drawer. The cabinet is very similar too.
Yes I would have the belt replaced. As to refinishing it that is a call you will have to make. The value is affected if it is not in good shape but if you want to preserve value don't do anymore than you have to. But how far you go only you can decide what you want it to look like.
I don't know how many of this era are available and that also affects the value. Look on line at sites that deal with renovating old Singers they can give you better advice than I can. And they will have access to any parts you might need.
There is another thread on the board about rebuillding an old Singer and someone put a link on there for Old Singer repairs. If and when I find it I will post it here.
I don't know much about the other machine.