Are there any readily available chemicals that can be used to test the presence of Ammonia, Nitrite & Nitrate in water ?

Well, the ways to test for ammonia, I was taught, was to boil the solution, where aqueous NaOH was first added to, and test for the gas produced (if any) with moist red litmus paper. If there is a colour change, you have ammonia.

Now, if you add aluminium to the solution after boiling, and you boil it again testing for ammonia, if you again get ammonia (you must make sure that there is no more ammonia in the previous solution before you start that though), that means that you had nitrates in the solution.

Okay, for nitrite now, if you add any strong acid and you see effervescence, and the gas released turns brown/purple in air, then you had nitrite in the solution.