Most corals that live near the surface will suffer without light. I would be concerned about them not having light for more than 24-48 hours.
A refugium will give you more water volume and that can help stabilise the conditions in the tank, but it won't make any difference to algae unless you have high nitrates or phosphates. Then the macro algae in the refugium will help keep those levels down and minimise algae. Because corals have a symbiotic algae living in their cells, they photosynthesise when they get light and help use some nutrients produced by the coral animal and in the water. They should also reduce the light getting to the rocks and substrate (by shading) and help limit algae in those areas.
Diatoms are slightly different and regularly grow in newly set up aquariums. After a few months they normally die off and get replaced by normal types of algae.
You can grow macro algae in coral tanks. I used to have feather Caulerpa, bubble Caulerpa and Halimeda in my tanks. Just don't let it crawl across the corals. A friend of mine used to grow turtle grass in his marine tank. Any macro algae you can get to grow in the tank will help reduce nutrients and minimise algae growth.
When dealing with marine algae, make sure the temperature or salinity doesn't fluctuate or change suddenly because it can kill them. If you buy some from a shop, make sure your tank has the same temperature and salinity and keep the plants out of the sun while travelling home.
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The liquid pH test does look like it's around 8.4, which is fine.
The salinity (specific gravity) could come down a little bit to 35ppt. Having it at 36ppt isn't a big issue but dropping it a fraction might help some corals depending on what the shop's water was before you got them, and where they originated from.
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There should be enough surface turbulence to keep oxygen levels up but you can increase it a bit if you like. Some corals like lots of water movement and others prefer less. Try increasing and decreasing a bit and see how it affects the corals.
You can drill a few more holes in the spray bar (filter outlet) so more water can come out. If you don't want to drill into the current spray bar, buy a piece of pvc pipe from a hardware store that fits on the filter and drill holes in that.