Is ingesting water during swimming harmful?
Could this be potentially harmful depending on the chemical content in the pool?


Probably not, unless you managed to drink quite a bit of pool water. Worldwide, millions (hundreds of millions?) of people have collectively ingested millions (billions?) of liters of pool water - with varying chemistries - over many decades (myself included), and nobody seems to have suffered too much. I believe this falls into the "generally regarded as safe" area.


  Are there studies which advise on the extent of permissible chemicals that can be added to a pool?


Numerous ones, Google away. These guidelines, from the State of Indiana, are representative of the recommended levels of various chemicals present in common swimming pools.