A refugium is a tank that is connected to the DT that houses different macroalgea's. The purpose of a refugium is to remove build up of Phospates and nitrates in the water. The area in the back of your nano is not a refugium but more of a wet/dry type of filter as where the sponge hosts bacteria...
Before you start making your way into reef tanks, you fisrt need to get a few bases covered. First is your lighting... You need 5+ watts of light per gallon of water. They make some nice retrofit lights with PC and MH in one unit. Second I would consider moving up to a wet/dry type of filter...
You might be pushing the mandarin a bit early as your tank need time to build up an abundance of copepods. They say you can get them to eat live brine, but from what I hear it's not an easy task.
Looking to get a small nano cube, maybe a 8 gallon... Any suggestion on a brand or model? Just starting to look into them as a second DT. Hoping to get something that closes up tight as I want to get a dwarf octopus.