Don't do anything about the nitrates. 3 is fine. Great actually. Most corals will do better at 3 then zero. Once upon a time a lfs sold me (not knowing) everything under the sun "fixing" problems I never knew I had. Or didn't have. I'm not kidding I spent at one point about a thousand bucks catering to a $100 dollar coral by recomendation by the lfs. I still have that coral lol. Point is, if you are a gadget person and like to tinker that's fine. But you don't need any of it as long as you don't overstock or over feed.. Which is easy to do, trust me.
If your nitrates are settled you should add a fish a month. Do your water changes accordingly. Since your tank is small, and water changes could be larger, heat the water and bring the salinity up. Once the bacteria is settled for the fish load add some corals. You might be able to add Zoas or star polyps now. I'm not sure exactly where you are at but I'm convinced fresh water wouldn't kill star polyps.
How bad is the algae really? Is it just ugly or it it getting out of control? Ugly, especially if you started with dead rock is normal. A snail will do wonders for that. Cut the lights down if you want but maybe not needed. Set them to be on for when you are home. Fish don't know when it's actually day time.