Most of the best available razors are made of carbon steel and if not cared for properly will rust.
One can use gun oil, camelia oil or any other rust preventive product by applying a thin layer after each use. I personally like and use ballistol. I also have a bottle of camellia oil at my disposal. For long term storage I definitely recommend ballistol as camelia oil can dry out and turn into a gunk substance. For daily or frequent use both work equally well.
Always make sure the razor is totally dry before applying anything.
When I shave with a straight razor I always dry the razor in between passes. After my shave I personally like to leave my razor in the open position after cleaning and drying, That way I'm 100% sure there is no humidity or water left between the scales.
Rennaisance Wax is another excellent product that can also be used to protect your razor especially for long term storage as it's invisible and not oily.
For water spots or black staining any metal polish will do. My favorite is simichrome. Black Magic and Maas metal polish also work great.
Be advised to clean up black staining or spots in the early stages. Once it turns into heavy staining or rust no amount of metal polish will help as once oxidation starts to eat away into your steel you'll have to live with shallow remaining residual surface pits and staining.