+ What color is the INSIDE of your toilet tank? (look inside a toilet that is white.)
+ Buy a small bottle of Iron Out in the detergent section somewhere.
+ Put a couple of tablespoons full in a thin small snack baggie; remove the air and close. (Do NOT suck the air out -- Iron Out fumes are better not breathed!)
+ Take the bag underwater, and open it onto one of the dark brown stains. Use the bag to hold over the Iron Out, so the slurry can sit there a few minutes without being wash away or immediately dissolved.

Dark brown (coffee/chocolate?) stains on a pool with well water sound like possible manganese stains - but I hope not. Gray green 'stains' sound like plaster mottling, which is a finishing problem.