Firstly I would clean the step down with a specific light alkaline cleaner, we have power clean , ( other brands avalible) dilute and use step by step with a white pad - rinse and towel dry, this will de grease the area.
As this stone contains iron traces , is this internal or external ?, washing with an incorrect product can advance iron oxides ( some acid based cleaners) or even moisture can cause a bloom,
The spotting can be delt with , but I would clean back and come back to us on what remains after this.