It's true that nano tanks can be difficult, but they don't have to be if you keep on top of them. Here's the thing with all reef tanks, the fundamentals haven't changed at all, but now we have better tools and we get more detail into each aspect. For nano tanks, the two main issues are heat and salinity, but with ATO's and better heaters/controllers, those can be managed without any major issues besides dealing with ambient room temp.
So, I'll start with what I think works best for nano tanks and I won't sugar coat anything, keeping with the theme of your tank.
I'm not sure about the history of your rock, but it doesn't look like there's much there in the way of microbial life and that's 90% of a tank's biology. But, with time and maybe seeding it with some seasoned rock/rubble from a trusted friend or with a little real ocean rock, will help establish some good stuff. Also, starting bare bottom is going to be a lot tougher in the beginning than using sand (seeded w/live sand). I also don't think your fish choice helped you much, as some of these fish require a lot of room or plenty of live foods, pods, micro fauna, etc... For nano tanks the best CUC are usally all snail-based crew with maybe one or two scarlet hermits. I like a mix of turbos (1 or 2 for your size) a few astraea, trochus and maybe a couple ceriths. I also wouldn't use any chemical filtration at this point, as you really need to build up your microbiome and chemicals works against that, especially in the beginning. I don't think employing a refugium at this stage is worth it and most likely not helping you at all, but just delaying establishing a healthy system. So back to your fish choices. The only two fish that work right now are the clown(s) and the neon goby, the rest are too specialized or simply too big or the wrong choice for your tank. Pipefish require an established tank with an endless supply of pods, micro-critters and there's no substituting their diet with artemia that's going to help them long term, they simply are a bad choice for your system in general. Trying to use fish for algae control in your tank is simply the wrong choice, as there are no fish that will be happy in your tank, that won't either die from stress or want to kill everything because they are too stressed from the cramped quarters.
So here's my approach to keeping nano tanks and also helping you get ahead long term. Start with your source water, either buy an RO sytem or buy water from a trusted LFS that has quality water, which is probably not many. I would use a 5 stage system at minimum, this would be a single membrane system, as you don't have to make very much water. I would use a hybrid filter set, which would give you the best water without spending a ton of money. I would use BRS sediment (GE, I think?), two universal carbon blocks, Dow 75 or 90gpd membrane, then use Spectrapure for the DI stages, specifically the megamaxcap, then the high capacity silica buster (color changing). The megamaxcap and the membrane would last the longest, so the only things you would need to change are the sediment, carbon blocks and the silica buster as needed. Next, I would choose a quality salt mix, despite what some may say, Tropic Marin Pro is still one of the best salts out there and my preferred choice. It's mixes up super fast and can be stored for a long time without any chemical/ion change at all. I would do a 15% water change weekly or bi-weekly based on your willingness or maintenance habits? I would also use TM All for Reef as your additive for replenishing your major and minor elements, it's simply one of the best things to happen to nano tanks. The water changes would be to correct any issues or for any elements that are building up or depleted. For the algae issue, I think elbow grease and the right snail mix will do the job, but it's going to take a while before it gets better, you just have to stick with it and ride it out. For fish, I would stick to fish that work in nano tanks, smaller gobies, clowns and smaller blennies, but not algae blennies or big herbivores. Take the fuge offline and remove all chemical filtration and rely on your elbow grease and snails to work on the algae. If you want to stick with a bare bottom, then I would get more live rock, not dry rock. You don't need much more, but a few nice pieces would go a long way in establishing a healthy tank. The lighting is fine, but I do agree that red and green should only be 5% max. I'm not a Blade fan, but I get their appeal, I just think they're overpriced. Luca from Quanta Lights will be releasing his fixture in May and I think it will be a great fixture for a lot of people, as he's the only one trying to use T5's and halides as his starting point for spectrum and coverage. He's truly trying to replicate the spectrum of a particular halide bulb and a mix of T5 bulbs, while trying to utilize the reflectors that make those lights the gold standard.
That's all I have for now, but there's tons more I can share, so ask away or simply ignore my post, as I have a habit of talking/typing for a while.
Go slow, stick to the basics/fundamentals and you'll be okay. Cheers!