I am so sorry about your loss. After you have a fish for a few years, they are really more like family ...
I don't know what those white balls are ....they may be ich cysts ... you can only identify that with a microscope. If they are cysts, that is a really heavy infestation ... and you may well have lots hiding in your gravel in the hosp tank. It is important to really vacuum out the gravel (or get rid of it altogether) to reduce the ich load.
Sometimes ich hide in the gills of the fish, and you don't see many external spots. If you have not disposed of Iggy yet, it would be useful to do an inspection of the gills to see if there are spots. The ich can get so bad in the gills that the fish suffocates.
I've had good results treating ich with salt in the past. Here's an article on how:
Goldfish and Aquarium Board Article-Treating Ich with Salt
A few additional comments:
1. bring up the salt level slowly ... 0.1% every 12 hrs till you get to 0.3%.
2. dissolve the salt in water first ... goldies like to eat the salt grains & that burns their mouth.
3. when doing water changes, match the current salt level in the tank as well as temp.
With a heavy ich infestation, it might be advantageous to do Ingrid's "tub to tub" method. You use 2 tubs, both with clean (dechlorinated) water of identical composition. You put the fish in tub 1 in day 1. Next day (or sooner if the water condition in tub 1 deteriorates), move him (& heater/filter) to tub 2. <Do not net the fish ... that is stressful. Instead, submerge a small bowl in the water & gently scoop up the fish so he is never out of the water.> Clean out tub 1 & refill with clean water ... so you are ready to transfer the fish back to tub 1 when tub 2 gets messed up. Repeat .....
Advantage of the tub-to-tub method is that you leave all the ich cysts behind so you don't reinfect the fish. Also, you take care of your water changes at the same time, and you always have a tub of clean water ready to transfer the fish into at a moment's notice. And with a daily water change like that, ammonia don't have a chance to build up, nor do you have accumulating waste at the bottom to give you spikes. <BTW, 0.25 of ammonia is OK, I won't stress out too much if you can keep it below 0.5.>
Some people do the tub-to tub for the entire duration of treatment, although I think that a few days of that until you significantly reduced the ich load is adaquate. I would, however, maintain salt level for at least 2 weeks after ich is gone, and then gradually reduce that back to zero over a few days.
As for the plant ... it won't survive salt. If it is valuable, you can sterilize it or QT it. Standard sterirization for plants is 1:10 bleach for 30-60 seconds. Then rinse really well with dechlorinated water. <Do not bleach the roots, and some plants like Vals & hornwort will not survive bleaching.> Alternative is to QT the plant. If you leave the plant in a tub without fish for 2 weeks, it should be safe to return to the main tank. Ich & mos tparasites cannot survie without a fish host for that length of time.