Should I rather treats single spots to conserve the original paint or go for a repaint with a restoration project?

Answering your numbered questions first:

1. Will the rusty/blank spots be a functional problem down the line?
   A: Bare steel will rust. It needs to be covered in some way to prevent corrosion.

2. Will power coating work well with the steel frame?
   A: Powder coating is an option that will work well on a steel frame. Here is a Sheldon Brown article that talks about the work involved in a full paint job and the different methods.

3. Is it possible to treat all the small spots where the paint came independently to preserve "the original"?
   A: Yes, it is possible to touch up problem spots, protect the bare steel and look nice. Here is a link to a professional bicycle frame touch up expert (not a recommendation) to illustrate what is possible in the world of touch up.

Full repaint or touch up? It depends on your preferences.
When making this decision keep in mind that no matter what you do a bike that is ridden will get scratched - it's inevitable.

Here are two ends of the decision spectrum...

• I'm trying to maintain the originality of the bicycle as much as possible - touch up.
• I don't care about originality and I'm willing to do what it takes to get a fresh paint job - full repaint.

In my mind a full repaint is a last resort.

• It's time consuming and difficult to do right on your own.
• It's expensive to have someone else do it for you.

Looking at your pictures my evaluation is that you can do some touch up / spot paint work and remediate most of your issues.

• I would not repaint the fork end. The paint will be scratched again when you put the front wheel on. At most a clear coat.
• the brake bridge is bare steel so it needs to be protected but it is also hidden so a clear coat would do the trick.
• Drive side chain stay is a candidate for touch up. Or, possibly a chain stay protector.

Personal choice, but as an FYI Testors model paint tends to work well for small areas and usually can be matched pretty well to bikes.