No, the ammonia and nitrItes will be zero. NitrAtes should be really high after a fishless cycle (i had around 100pmm after my last FS), and that should be reduced to something reasonable (i try for under 20ppm) before adding fish. As for how to test for nitrates, you need a test kit for nitrates.So, after my nitrates and ammonia are at 0, can I add my fish after a water change?
Just to clarify, the cycle goes like this ammonia ---> nitrites ---> nitrates
Nitrates are the end product of the nitrogen cycle. In a natural system they would be used up by plants, in most home aquaria with little or no plants, the nitrates (and other dissolved stuff that we can't test for, like hormones and such) have to be diluted with regular water changes.
And yes, once there is zero ammonia, zero nitrItes, and low nitrAtes, you can safely add fish at that point.