I don't know for sure...so these are just my thoughts.
1) I wouldn't be worried about the cooling water flowing from the P hole. Typically a motor moves PLENTY of water through that hole to sufficiently cool the engine.
2)Performance shouldn't be an issue either, as it sounds like you are moving lots of water through the pump and out the nozzle.
On the other hand, what you describe is not normal. It absolutely sounds like you are missing a gasket, and if water is leaving from where it shouldn't be, then it is definetly entering where it shouldn't be. Get it checked out soon or you might risk bearings in the pump.
Dan