Hard to tell for sure by the pictures but that’s what it looks like to me. Maybe rub a chlorine tab on it to see if it breaks it up or try some black out treatment. 

What is the surface of the pool?  If plaster, then this possibly is black.  If this is pebble sheen, then I would say the water seems aggressive, and could be simply wearing down the skim coat on the pebbles.  That will leave excess main color pebbles to be coming through.  In short, the black pebbles in the color mix are overpowering the fine color stones, and leaving a discoloration of the entire surface.

No that is copper staining, use some citric acid on it or take a pipe and use muriatic on it and it’ll come right up.  There is also a tool you can use that attaches to the pole and has a cup on top and pad on the bottom.  You can put muriatic in there and sit it right on top of the stain it’ll take it up in minutes.   

If there is a heater it may have a bad core causing copper to get into the pool.  You will want to use some metal out regularly.  When copper is present if you use granular chlorine it will stain the surface wherever you spread it.  Happens almost immediately. 

This is exactly what I thought it was. I haven’t had a chance to get by there yet myself to correct the issue but will be early next week. I think this homeowner tried to correct the green pool he had himself before hiring us and he likely poured in some copper-based algaecides into it. I’m going to try and look up that tool you’re talking about and see about ordering it. Thank you.