you can clean the rust using BKF (bar keepers friend) found @ Walmart and any other general store, grab a nylon or bristle brush and scrub with it. Rinse very well because its acid based, then dry well.

The stone is Karasu, and they are supposed to be the finest for finishing blades. Karasu are very hard therefore scratchy, when you practice on it you will discover the right amount of pressure and slurry for best results.