The hair algae is not your biggest problem but the cyano means you have some feeding issues. Cyano is bacteria, not algae and it will not help you in any way so it is best to be rid of it. A little of it is normal in places like between the glass and substrait or at the base of certain corals but if you have a lot of it that is a problem. I am quite sure you are feeding way too much and probably too often. I have about 25 fish in my tank and they get maybe a small cube of mysis 5 times a week. Many of my fish are breeding so I know they are well fed. I feed other things but I wanted to demonstrate the amount of food. A fishes stomach is about as large as it's eye and doen not have to be filled each feeding. Yes I know they are always hungry, so am I.

You need to remove as much of the cyano you can manually. If you shoot a canister filter at it it should come off to be cleared out. Then feed much less and skip a day twice a week until the stuff is gone.
The algae is a different story and I just posted a long post on another thread which I will paste here, but in a new tank these things are normal.
Being you have both cyano and hair algae you will need to change some water after you siphon out the cyano.
Quote
"Unfortunately Hair algae is a part of this hobby but it is not a disease and it can not be cured. It grows on healthy reefs all over the world. Of course we don't want it covering our corals but if you only see a little of it, don't worry about it. If it is growing all over the place you can not really control it with animals. The hair algae just comes out in a little while as algae fertilizer. This works in the sea where there is unlimited water volume to disapate the nutrients and most of that is much too deep for algae to grow. In the sea there are uncountable tangs to eat it diring the day and at night urchins crawl out from everywhere.
(I have been diving at night for many years and have seen this many times)
Algae actuallty makes the water better and if you do not see any algae at all, your water may not be as healthy as you believe it to be.
You can eliminate the hair algae but it is time consuming. It will leave on it's own as soon as it depletes the nutrients it is living on. When that happens, it will die overnight and you will think your hermit crabs or sea hair ate it all, they did not.
You can speed up the process if you manually remove the hair algae where you can and do not change the water. Yes I know what everyone will tell you but changing the water at this point will just fuel more algae. If you pull out the algae along with the incorporated nutrients, very soon the algae nutrients will be exhausted and the algae will die on it's own. Then you can change water and in the future, feed less, rinse frozen food and remove any detritus you can see.
This happens to new tanks and it is normal. Eventually the bacteria population in your tank will settle down and the correct types of bacteria will grow in sufficient numbers to control the nutrients to an extent that you barely have any hair algae.
My tank is 40 years old and I occasionally see some. It leaves on it's own and I consider it a good thing"