Nitrate Control

The best long term solution for nitrate control is algal uptake. I highly suggest a refugium if that is possible. They also make small in-tank refugia that may help some. There are also other options, such as turf scrubbers, but that may or may not be easy in your situation. You haven't really described your setup in detail, though. Do you have a sump? Can you fit one, etc.?

Beyond that, the blue tang really needs a much larger tank. Also, while it isn't necessarily natural or optimal, 20 ppm of NO3- is still considered acceptable in most circumstances. However, with the solutions above, you can reduce that, as well. In addition to that, how often are you changing any mechanical filtration, if you have any?

The main thing with the tang is that they like lots of swimming room--not something your tank is going to be able to provide. They are best left to much larger tanks, unfortunately. As far as replacing the media, I highly recommend you change the mechanical filter more often. Every 2 months is very inadequate under almost all circumstances. If you are experiencing a nitrate problem, changing this more often may be a bit help, in addition to the refugium. I also highly recommend looking into a sump where you can place a protein skimmer and/or a larger refugium to help you deal with the excess nitrogen. The refugium will be more effective at directly handling nitrate than a skimmer will, though.

My guess is the mechanical (sponge and carbon) and bio media (biomax cartridge)that came with that the AC filter is the cause of your problem. Think the biggest problem may be the sponge even though you are rinsing the sponge between change outs. I had a similar problem with sponges in my old Aquapod. I ditched the sponge and bought a huge bag of Poly-fill from Walmart (fabric section, its pillow stuffing) and I replace it once/twice per week. The bag is about $4 and it will last you forever. Just make sure to avoid the flame retardent stuff if your WM happens to carry that. You can buy the same stuff as Petco, Petsmart, etc but it will cost you a lot more for a lot less material. I have a AC filter as well and just lay a mat of the fill down on the bottom of the tray and then place a bag of Chemipure Elite on top.

I'm guessing your carbon may be a problem as well. A bag of carbon in a tank with larger fish will get exhausted pretty quickly and once its spent, nutrients will just leach right back out into your water. I would change the carbon twice per month or go buy some Chemipure Elite which will last you 2-3 months between changeouts. Also ditch the biomax cartridge, your LR is providing all the denitrifying bacteria your need. That little bag isn't doing much more (except probably trapping detritus).

A for refugium options w/out a sump. You could modify your existing AC filter into a HOB fuge. Lots of reefers have done this. I think an AC 50 might be a little small. Most use a 70 or 110. A 110 on that size tank would provide some nice flow as well. Speaking of flow, do you have enough in your tank to keep detritus off your LR? If not increase your flow with PHs or maybe upgrading your filter to the 110. Ever use a turkey baster to blow off your rocks? Trapped detritus in your LR may be part of the problem as well.

You're going to want to find a new home for that tang. They're swimmers and need lots of room.

What are the nitrate concentrations from tap? Topping off with RO water and then going and performing 10-20% weekly water changes with tapwater isn't doing you any good--if anything, it is a waste of money. Step up to replacing and/or rinsing that sponge on a weekly basis, if not more. Carbon schedule sounds good and the water change schedule by itself does, but see my point on tapwater. You don't need to tear down the skimmer and clean it monthly, but you should be cleaning the neck and riser portion of the cup almost daily. I recommend a toothbrush to gently circle around the neck and get rid of any buildup. This accomplishes removal of buildup without disturbing the action of the skimmer. It should help it get more consistent skimming.

What's in the cup isn't as important (unless you are sensitive to the smell). What is important is that you break up some of the scum that develops on the inside of the neck. You don't want to completely clean it (i.e. squeaky clean) every time, just a quick brush with a toothbrush. Then, every month or so, or when the cup fills, take the whole thing off and clean it thoroughly. You just don't want to do that too often because it does interrupt performance for a while.

As far as your water change regimen is concerned, in theory, that is right. However, you don't know what else is in your tapwater. There could also be compounds created in your tank that aren't necessarily getting diluted that you are simply adding back during a water change. Don't ask me what exactly those may be specifically (organics are likely), but it is something to consider. There are a lot of variables out there, and I don't know if you are like me, but I like to reduce them as much as possible. If I can throw out one more unknown in all of this, I'm happy. JMO.