It is disheartening when you lose a fish, or any creature in your tank for that matter and can be frustrating too if you're struggling with nuisance algae.
Personally, I think you should set out in your mind what it is that you want to achieve with your aquarium and then make yourself fully aware of what will be involved in attaining and maintaining your final stocking. At the moment you seem a little undecided and frustrated (we've all been there). Fishkeeping should be enjoyable and having an end game and a plan of action on how to go about achieving it, will definitely take a lot of the stress out of it. In your first post it seemed that getting rid of the hair algae was your main priority but your last post shows that keeping an urchin is actually what you want to do.
With that in mind, adding an urchin certainly is possible to do in your tank. At the moment there is an abundance of food readily available for it. What people were pointing out is that if the urchin eats the algae faster than it can replenish itself, then it will gradually starve to death (as will your mithrax) unless you supplement its diet with dried seaweed. This isn't a problem, as its just a case of adding a strip of nori into the tank - probably best done by attaching it first to a small piece of live rock with a rubber band or something like that. That way, the seaweed won't be moving around the tank and the urchin will be able to reach it. You could also try placing or holding the nori in its path. Alternatively you could try algae pellets, like those that are commonly fed to freshwater pleco's.
Pin cushion/tuxedo urchins are better for a nano tank as they only grow to around 3" in size. A pencil urchin can grow to 5", so purely from a size aspect, the tuxedo is the better option. I also think the tuxedos are significantly more attractive than pencil urchins. I've had a pencil urchin before. They are rarely seen as they hide when the lights are on and when they are visible, they really aren't the prettiest thing in the world lol.
If you do add one, then you will need to perform water changes. One, to remove the nitrates that may build up as a consequence of the hair algae being eaten. Secondly, it is highly likely that trace elements in the water will need to be replenished in order to maintain its health. At the moment your tank has reached an equilibrium, in the sense that the ammonia and subsequent nitrate that is produced by your fish is consumed by the hair algae down to non detectable levels. Obviously, as this gets eaten, and knocks your tank out of equilibrium, the NO3 levels will begin to rise and you may find that cyanobacteria spreads all over the sandbed or you're forever cleaning the glass.
If you have your heart set on an urchin then I'd suggest that you pick up a nice red or blue tuxedo. Plan ahead and purchase some nori, for when the time comes to suppliment its diet. I'd also get some Chaetomorpha. If you don't have a sump, then you can simply wedge it behind the back of the rocks. This will compete with the hair algae and help prevent other nuisance algae from gaining a foothold. Its not the most attractive stuff in the world but, it will consume the nitrates and phosphates in your tank.
