Good to learn that your Snake Plant is doing better, Chelsea! This is a plant where doing less is almost always better; it thrives on neglect.
Definitely, do NOT replace the soil. If you do, you will set it way back. the soil is dusty because you are allowing it to dry out in between waterings, as you should. It also does not need fertilizer. As I said, less is more with this plant, with the exception of sunlight.
The spots you see are blemishes and have no specific cause that can be remedied.
