Generally there is a high spike before you will get cycled and it sounds like that is possibly what could have happened.
Some times if a fish is stressed or ill and there is a spike in the parameters it is enough to push it over the edge and the amount of Nitrites or Nitrates will be fatal.
Possibly an older fish, possibly it was being picked on already. How many of those are in the tank, maybe you have more males than females and they were bothering that one?
Yes that was bad advice to ditch the media at least in the filter. Upgrading a filter can be done and save the existing media using it in the new filter or running the two filters at the same time for around a month to build BB in the new one. Although not as much as the filter the gravel has BB too, just removing that can also cause a mini cycle.
As for the igloo. The sand or gravel under the igloo will se a reduction in oxygen so could stagnate. It would be good to vac the area on a regular basis to get food scraps and waste build up from under it.
Also I use the alternating cleaning method which is clean one area in the tank at a time (each week or when you do your cleaning out):
Treated water filter pad rinse, if the pad is in horrible shape I add another new one to piggy back with it an give it a few weeks to build BB. I actually prefer to use 2 pads anyway to give it the optimum possible area to grow BB!
Whole filter clean the housing and do not clean the pad
Glass scrub (rarely needed)
Substrate vac you can even divide this in half one day and half on another week
As for the algae try leaving the light on a little less time and splitting the lights on and with a few hours of no light on in the day, aka split photo period, or siesta. Picking it off is fine to add to that process.