Your heart is absolutely in the right place. ... AND I don't want to discourage you.... however, ...IMO, .. I do not see enough LIVE rock in your tank to be trying to keep corals alive yet. I "think" you need to relax and back off a bit. Let the tank mature just a bit more and it would be a good idea if you could place one nice sized chunk of for real live rock in it. Also, what is happening in that HOB filter? If that is a fresh water type filter it is not impossible but IMO will be very difficult to maintain coral. Sorry, but I can't tell enough by the picture. You can get there and it is worth the effort, but I think you are pushing the time line a little too hard. I'd consider working with the tank and nature rather than pushing it. The old adage "you can't fool mother nature" has a lot of truth in it. "Mother Nature" will win.
If you don't have one, shop around for a small skimmer to hang on the back. If you can't afford one there are several u-tube vids on some ways to DIY one. IMO a skimmer is almost necessary to keep a salt water reef tank. It mimics what the surf white caps do in real reefs with the foam. It is part of the natural filtration methods. The other half of that picture is lots of "living" live rock. With these you don't need a hang on the back filter to fuss with and maintain.
Also, IMO you should have a fish or two for the natural balance of things. I am wondering if your tank has actually cycled yet... maybe I missed that part.

If you aren't sure it has cycled post some testing results so we can help with that. Please do not add any fish until we can decide that you have cycled.
If you started with base rock alone it can take as long as several weeks to get a good cycle and live rock balance achieved. ... And that is fine, things happen very slowly in a reef tank. This is one of the things that make them good for us, they bring us back to a slower more relaxed state of mind.
DON'T give up.. but do slow down, relax, and enjoy the ride. It is much less stressful if you just go with the flow and let us lead you along.