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I'm afraid what you call dark areas are actually corrosion i.e. pitting. They need more abrasion than a soft cloth & polish can provide. Of particular concern is the area near the heel on the razor...

That would really depend on your skill & experience.

Always hard to judge from pics but...
1. Rust on the edge is always bad but sometimes you can hone beyond it. The rest can be removed to varying degree.
2. Yes it is possible to clean without...