"Cleaning" LR?

The chunks of stuff are probably dead stuff from the uncured live rock. The brown stuff could be diatoms which could be normaly during early stage of the tank. If your rock's collecting all that stuff to the point where you can dust it off and the water becomes cloudy, you probably want little bit more circulation, at least more directed around the rocks. Make sure you have enough circulation around the rocks so that these things don't collect. It's inevitable and will find places to collect, but try to minimize it. After you "dust" off these stuff, I would do some more testing again to make sure that your ammonia and nitrite still remain at 0. More than likely you will have high level of nitrate from all the broken down dead stuff. I would even try adding pure ammonia to see if the cycle's completed. After that, do multiple partial water changes to bring down to that nitrate to near 0. Then I think you might be ready. It's good that you are taking things slowly. Stay patient, and good luck!