Please help me zero down on my grayish deposits on my pool floor

How do you chlorinate your pool? The round pattern in the first and third photos appears to be about the same size as a three-inch trichlor tab. They are acidic and can etch/discolor the surface. Has anyone ever allowed a tablet to sit on the step?
 
I use dichlor powder. There is some impression from stones which fell in pool over the winter - a few of them. That is not my major problem.

I get a lot of dirt - from air, surrounding. These look like dirt to me. but trapped in something...
 
Looks a lot like mine. Slight chemical etching of the pool surface coupled with metal deposition. Used to have a Frog system. System continuously suspended metals in water. Thinking it was some form of mold, added more chemicals (most metals based). Bounce when shocking, as recommended by builder, deposited metals on white plaster, resulting in a “mottled” look. Have learned to live with it...
 
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