It sounds like you are describing efflorescence or a mineral deposit. It would be easier if you send a photo. If it is at the water line it's most likely calcium deposits. If it's at the edge of the pool it's most likely due to water seeping out. (efflorescence)
limestone has a white streak.
A streak is the color of the powdered mineral left behind when the mineral is rubbed against a hard, rough surface. Limestone typically has a white streak due to its composition of calcium carbonate.
White.
Limestone can and does appear in shades of green, due to impurities.
When limestone (CaCO3) is heated, calcium oxide is produced!
Pure white limestone often forms in areas where the limestone has experienced very little exposure to impurities or contaminants during its formation process. This can happen in environments such as deep ocean basins, where the limestone can accumulate without being mixed with other sediments or minerals.
Sand it down and paint it.
Limestone can come in grey, yellow, white and a bunch of other colors too.
Possibly over time, but nothing you should notice for as long as you own the pool. You will however see a white residue on your nat. stone. This is caused by splash out. The water on the pool deck will evaporate, but the salt will not. This is easily cleaned up by hosing off the spots with tap water. If you do not clean them off in a timely fasion, it may cause excessive build up, which will have to be acid washed off.
Croatia
Polished white limestone.
Calcite.