++1 on the previous advice. Never store your straight razor in the bathroom. I keep my razors as well as my strop in my bedroom.

You can purchase some Maas or Semi-Chrome metal polish to remove most of the rust/corrosion pictured on your razor. It will remove some of the etching on your blade, so go slow when performing that operation.

Finally, apply a thin coat of oil to your blade after use as suggested in one of the previous posts. I used Tuff-Glide in the past. I now use Ballistol spray.

Good luck!