I did a quick read on your entire post and I see few things that really not needed to be fixed or at least one issue at a time.
1st why are you trying to play so much with chemical imbalance in your tank..is it full of SPS or LPS? If not then leave the chemicals and the testing out for now till you fix the other issues.
A broken heater could lead to few problems one possibly a bacteria bloom.remove the dead heater do a water change, replace your Activated carbon and make sure your skimmer is running properly.
I think your cloudy water started by chemical imbalance by your doser crapping out then it lingered few days as you kept trying to fix the imbalance,..You cannot see your fish so you probably added more fish food more often for them to survive, from doing so you created alot of proteins running in your tank then the bacteria bloom started taking over and you still have it mixed with chemical imbalance and nothing will get better unless you take it one step at a time.
Most replies are above are great for getting your chemicals properly in check.
Take slow and I mean very slow.
Tune down your lighting period or percentage, replace the Activated carbon, fix the skimmer, keep temperature between 78 and 80 degree (slows down the bacteria bloom), do a couple water changes directly from and by over driving your skimmer (wet skimming), keep feeding your fish as you did in the past, less food is always best as you want the fish to scavenge around your tank, of course keep the tank turn over as much as possible (the more oxygen the better)
in no more that 10 days (max) and your water should clear out fine.
then go ahead and tackle the chemical imbalance again very slowly.
Hope that helps
