You know your tank is cycled by testing your water. 0 Amonia, is the key indicator here, once that hits 0 you can add live stock. Other tests that should be done as part of your mainenance are, Nitrate, Nitrite, pH, and Salinity. Also keeping an eye on your temperature and take notice of any substantial swings in temperature from morning to evening.
Diatoms show up when a tank is set up and running. As to when to expect them? That cannot be given a time line, they will show up as part of the growing pains of a newly set up aquarium. However after this process is complete you should see this bloom disapear. If it does not go away in a few weeks there are other things to consider that could be a cause as to why. Using tap water instead of RO water, over feeding too many nutrients in the water. Hope this helps...