To add to the above list, since I am thinking the tank is cycling as well, please test and post results for ammonia and nitrites as well. You may already know this, but new tanks go through stages of algae. Usually first is the diatom bloom (brown algae that will cover all rocks and sand; will last for a couple-few weeks until all silicates are used up), then comes the green hair algae. That can last anywhere from a few weeks to permanently depending on your water quality, bioload, etc.
The brown on the first picture looks like diatoms. The brown stringy algae on the second could be dinoflagellates (hopefully not!). Can you post another picture of the Zoas?