those looks like very common green hair algae. very common in a young tank.
you also need to understand that the nitrate and phosphate levels that you are testing only show how much is remaining in your water after all the organisms (corals, algae, bacteria, etc.) had consumed what they need. so, while an elevated No3 and po4 levels may suggest that it'll cause algae issues, having "perfect" parameter levels doesn't mean that you'll have less algae issues. in fact, you can have 0 no3 and 0 po4 and have a huge algae outbreak (b/c the algae has consumed all the nutrients).
it looks like you are trying to raise corals too, so limiting waste (either by aggressive filtration, reducing light/feed, etc) really is not an option b/c since algaes are simpler organisms than coral, they tend to grab the available nutrients faster than corals. so, then it just becomes a numbers game of how much or how fast a "good" organism (coral, beneficial bacteria) can absorb the nutrient vs how much/fast the bad algaes can. in a young tank like yours, the bad currently significantly outweights the good.
the tried and true methods are therefore:
1) keeping up with your water change to at least remove the "excess" leftover nutrients b/c right now its fueling predomanantly the "bad" organism.
2) things that eat algae will help combat the bad population (but remember they poop too, so it's only a temporary solution that "delays" the nutrient cycle, excluding the small amount of nutrient that gets locked up in their own biomass as they grow)
3) manual removal
4) get a refugium - a strange of hair algae growing in the fuge is 1 less hair growing on the display tank
5) most importantly - time: keeping this up and eventually the "good" population will start to become bigger than the bad and will be able to out-compete the algae: ie:
a) your rocks are covered with coraline - bare rocks like what you have are prime real estate for new organisms to settle on, and algaes are the first settlers. Eventually coraline will take over which will limit where algae can grow.
b) coral biomas increase and eclipse algae biomas
c) beneficial bacteria reach sufficient diversity and stability.
keep up the hard work and it will eventually pay off. unfortunately there's no real shortcuts here for long-term and permanent algae control other than letting the tank mature.