At this stage of your tanks developement, there is little else you can do but water changes. NNR
takes quite a while, many many months. Sometimes over a year depending on the setup. As far as the cycle, if ammonia and nitrite are no longer detectable, the cycle is complete.
What you are refering to is a complete nitrogen cycle. Technically speaking, enough facultative/anaerobic bateria form to consume the nitrate and leave nitrogen as a by product.
An interim "fixes" other than water changes is setting up an algal scrubber/refufgium. These algae when harvested after some growth will also remove the waste products with them Simpley growing them is not enough, they must also be removed.