Lots of great advice that I’m just seconding here! All the guys above are on the money.
I agree; do a few 50% water changes. I like to just wait 48 hours (but 4-5 days in between i support) between these big changes when fixing past clients and friends tanks. But also make sure that you’re pre-Warming your new saltwater to minimize the temperature swing during the water change.
RODI units are great! And I also use a single 32 gallon brute can for my combined 150g, 35g, and 20g reefs, plus the acidic plants in my small greenhouse. To answer your question on storing water; I like to keep the 32g can at least half full at any time to solve any surprises.
Unfortunately, those two fish didn’t belong in that tank, especially dory. Blue tangs should have a minimum 6’ long 180g... and I wouldn’t put small one in even a 75g unless I had a concrete plan to get an appropriate tank within year. I’ve seen small fish quadruple in size in this time frame. While nitrates may have been a strong contributing factor, stress from insuffient room to swim, small-tank temperature swings, and low oxygen availability may have also contributed.While the skimmer will help a lot with oxygen, we must remember the very small surface area we’re dealing with.
Definitely keep your protein skimmer. That said; I’ve yet to see any nano-skimmer perform at even 10% of what I would expect from a comparably sized conventional in-sump skimmer. Keep that in mind before you put fish in there that have high bioloads.
How did the nitrates get so high? Most likely, this usually means there has been over feeding. And personally, I don’t like feeding corals often in Nano tanks. Just because nutrient export is so much more difficult.