salt is worthless in whatever treatment
I'm sorry, but this is not true. Depending upon the disease, and the fish species, this is often the most safe treatment.
The photo of the cardinal shows ich, or white spot. It is impossible for me to tell from the photo if something else may be present, but it is not uncommon to have fungal issues with parasitic disease, as the parasites are burrowing into the cells. I cannot see anything on the panda cories in the later photo. But if you say there are spots on other fish, this would seem to be ich.
Heat speeds up the cycle, so increasing temperature is useful. Some advocate heat raised to 90F/33C may kill ich over a week or two. But not all fish can withstand such high temperatures, and your panda cories are one; cardinals would be OK. But don't net out the cories, as they may be carrying this (as may every fish in the tank) and you might as well treat the tank effectively.
The safest and most effective treatment is plain salt, sodium chloride, such as Aquarium Salt or even sea salt provided there are no additives. Not table salt, and not marine salt. I had a particularly persistent parasitic issue (not sure what it actually was, possibly ich or velvet) that lasted over a year and a half, on and off, and I sought help from Dr. Neale Monks. The treatment I will outline is from him.
Raise the temperature to 30C/86F. You can do this partly with a partial water change (a WC should be done at the start of this or any treatment, generally) plus turning up the heater(s). Salt can be added at the level of 2 grams per liter. A level teaspoon is approximately 6 grams, so this treats 3 liters of tank water. Add this gradually, over half a day. Dissolve the salt first in hot water (dissolves faster in hot water) in a jar and pour it in; do not add salt crystals as these can burn fish. Take into account the displacement by substrate and decor, being careful not to overdose. Monitor the fishes' response and if you see obvious signs of stress, do a water change to reduce the salt. I've never seen this, but it can happen if you overdose accidentally.
Maintain the heat for two weeks. Do a partial water change after one week, and add sufficient salt only for the replacement water. At the end of two weeks, turn the heaters down to normal and let the tank water cool naturally. The salt will eventually be removed through normal weekly water changes.
I have used this on very sensitive wild caught fish, characins (including cardinals), cories, loaches, Farlowella and Whiptails. I have never lost a fish. I don't know what other fish you have besides cardinals and panda cories, but this treatment, according to Dr. Monks, is safe, and that was my experience. Salt is far safer than most of the ich remedies, many of which contain copper which is much more devastating to cories and characins.
Ich first attacks fish in the gills, so we don't see it; flashing may be the only evidence, but flashing can be a symptom of several issues, so don't jump to conclusions. But here there are external ich spots. Once you deal with the ich, there may be no need to go further. I am not certain of anything else besides the ich, and treatments are stressful on fish so you don't want to overdo things.
Byron.