My understanding of cyanobacteria is that it is caused by organics, period. This has certainly been my experience, both the recent issue I've previously mentioned but also a fairly severe bout in a former tank. Nitrates on their own will not cause cyano. However, nitrates are usually high if organics are over the limit, so it is easy to see a parallel. But one shouldn't lose sight of the fact that it is the organics, not the nitrates, causing cyanobacteria. Light does not cause it, but it needs light being photosynthetic.
And cyanobacteria is not an algae, it is a bacteria, just in case there is confusion there, since we have been dealing with both in this thread.
On the cloudy water, this is caused by bacteria, and they feed on organics. So we're back to the high organics. I explained this in my article on bacteria here
so all I'll say now is that the bacteria feeds on organic matter which can be waste or it can be DOC (dissolved organic carbon) which occurs even in tap water for example, which is why one almost always has a bacterial bloom in a new tank. See the article for more on that. And here again it is not ammonia causing this, but ammonia often occurs as a result.
We sometimes confuse things, incorrectly assuming the reaction is the cause. I think it is important to understand the root cause of these issues, since that is the only way to effectively deal with them.