When was the last time you replaced the filters in your RO/DI? You should be getting 0 TDS out of that at the end, that 3 ppm that you're getting has all the minerals and pollutants from your tap water still in it. Over time those will build up in your tank. Those chemicals could be benign, but they could also be... not. I'm not going to say that it's the cause of your problems, but it probably doesn't help.
Other than the corals, what fish do you have in your tank? What type of corals are you primarily interested in keeping, long-term? The answers to these questions might change my advice to you.
Based on what you've shown, this would be my plan of action for you:
First: Replace whatever parts of your RO/DI system you need to produce 0 TDS water. Your tap water contaminants may or may not be causing you problems, but they probably are and it's best to eliminate that variable. So whatever you need to replace here, do it.
Second, figure out your solution for the aiptasia. They're the most persistent pests you have in your tank and the hardest to address with simple husbandry, in the sense that just improving your habits won't do anything to them. You have options here, depending on what other animals you have in your tank. Peppermints will (supposedly) eat aiptasia, though I personally have never had success with them. Berghia nudibranches can be a one-time solution, but they'll usually not get all of your aiptasia before eventually starving out, and they might themselves be eaten by peppermint shrimp. Either an aiptasia-eating filefish, Australian Stripey or Pyramid Butterfly could also work in your size of tank, but all of them present some risk of also eating corals. Finally, there are some chemical methods you can use, such as kalkwasser pastes. Aiptasia can be a long-term problem with your tank, so decide how you want to address it and start working on it.
Third, add some herbivores to your CUC. Easiest thing to do is to go to reefcleaners.org and select a package. Pick up the diverse CUC - it'll include an emerald crab, which is one of the few animals that will eat bubble algae. You already have a tang in your tank, and he'll be the workhorse. But he can't do it all on his own, so the extra CUC will help him stay on top of it.
Fourth, do as much manual removal of the long hair algae as you can. Long strands are tough for your CUC to eat, so if you keep things short they can prevent the algae from growing longer. You can and should also use a turkey baster to blow off your rocks on a regular basis.
Finally, get yourself on a regular water change schedule and stick to it religiously. 10% a week is a good long-term plan, 20% a week can be suitable for getting over problems like this.
For other concerns:
Personally I'm not in favor of removing sand from an active tank. You can do it, but it's very easy to do too much, and sand can trap some really nasty stuff in it, especially if you don't have any animals that stir up the sandbed (like conches). If you do this, do it VERY slowly, and only take a little bit off the top of the sandbed. I speak from experience when I say that messing with your sandbed can kill your livestock.
UV wouldn't hurt, but it wouldn't do much to the hair algae. It might help with your film algae, and if you have dinos it will help with those.
What likely would help is adding an algae turf scrubber, but those are a big step up in expense and you should be able to get everything under control without one. The Santa Monica Surf2 (which is what I have) runs about $300. I am a big believer in the turf scrubbers, but not everyone has success with them and you don't need one to beat algae.
Finally, like I said in my first post, more flow is almost always a good thing, but don't add it with the expectation that it will help with your algae problems. Add it because it will benefit your corals and your overall tank health.
