You seem to be i a bit of a pickle. This is going to be a long post...
Let’s start with the fish.. all fish need to be removed from coral tank, and this must remain empty for 80 day (72 min). I don’t know how your “fish only” tank is set up, but depending on this, you may be able to add fish from coral tank to this and medicate that tank..if not you will have to remove all fish from both tanks into a separate tank, but this will need mature bio filter (which you could get from either tank, sponge floss etc) -I need more details of your setups...
Fish should be treated with a h202 dip on the way to the QT tank if you can. As this will alleviate immediate issues temporarily..
I would then use copper and api general cure together and that will sort fish problems.
As for coral tank, you have high nutrients else algae wouldn’t be growing...by removing the fish to a qt this will help reduce nutrients in the coral tank for the time being...I would use this time to do some watercahnges. (Don’t go crazy, just 20% a week to get the tank back on track-make sure to parameter correct the waterchange wateralso) this will reduce nutrients further, but you must still feed a small amounnt To the tank during the fallow period.. as for KH swings are you using a doser or calcium reactor to maintain all and calcium levels, (also what is your mag reading)
Aiptasia products only end up multiplying them...I had great success with a copperband and but I DO NOT suggest adding one with everything else going on
I’ll leave it here for now, and await further details / questions from you