Hair algae, means the production of nitrate--with ammonia at zero--means the cycle is completing. It by no means indicates "stability" or how it will respond to changes, such as adding bio load. I firmly believe, higher lifeforms are being added far too soon, in systems with incomplete cycles, and underdeveloped bacterial populations. You need to see the ammonia spike, followed by a Nitrite spike (if you feel the need to test for nitrite, and i suppose for cycling purposes you should.) Following that, nitrates will rise steadily. Autotrophic bacteria take 15 - 24 hours to reproduce, it is not likely that you would miss an ammonia spike, unless you were not paying attention. If you are reading 0 nitrates, you need to consider new or different test kits, which could possibly explain missing the spikes.
With fish in the tank, (or other higher life forms,) you cannot safely spike the ammonia, (unless you consider them sacrificial) to get your bacterial populations where they need to be initially. Such a system will take a considerable amount of time to stabilize, if it does.
Water changes do affect the Nitrogen Cycle, as it lowers the concentrations of ammonia and nitrite--as well as nitrate. The ammonia and nitrite concentrations will affect the growth of the bacterial populations, by taking away the food source needed in a reproducing population.
By artificially keeping the ammonia level down (water changes--to keep your fish alive) the bacteria population will not increase, and the threat of an ammonia spike will be ever present, till the spike occurs, and takes out your tank.
Adding a cycling aid (most are heterotrophic bacteria) will, most likely, cause the ammonia spike.
I firmly believe, after reading increasing numbers of "I never got an ammonia spike" posts and comments, that fully cured--so called "live rock"--does not have enough live about it to cycle a tank; and packaged "live sand" has nothing but heterotrophic bacteria in it, that will not seed Autotrophs, to speed up the development of healthy nitrifying bacterial colonies.