[WorkinMan]

If the live rock was fully cured it will have already been colonized with all the biological bacteria. That is why your nitrate has gone down to 0.
Deep within the confines of the rock there is water that is very low in oxygen, so low there is almost no oxygen at all. It is in these conditions that the bacteria that converts nitrate to harmless nitrogen gas thrive. You should be seeing bubbles coming from the rock. These bubbles are the nitrogen gas that the bacteria is producing.
The reason you saw an ammonia and nitrite spike after adding the live rock was becuase there was some die off (of whatever life was on the rock when you purchased it) that happened between when you purchased it and when you got it home and into your tank. This die off produced an amount of amonia that was too much for your current biological filter to handle, thus the reason for the spike. Now that those levels are back down to 0, it means that the bacterial colonies have increased in numbers to be able to handle the extra bio load that you placed on them when the new live rock was added.
This stuff gets confusing, so the best thing to do it search the net for the nitrogen cycle in saltwater(or marine) tank(or aquarium), and read, read, read. Then repeat daily untill you can spout it in your sleep. Good luck! Hope this helped!