No need for the salt.
You ran the tank for 4 weeks then did a partial water change. There was no need as nothing would have happened in a tank with nothing in it up to that point. The cycle doesn't start until you add fish or ammonia of some sort.
You then added 14 fish which was way too many at once in a new tank (the 4 weeks empty don't count). The ammonia levels etc would have gone skyhigh, resulting in the deaths you experienced.
They are obviously still stressed, probably from the ammonia, which is why they have whitespot. I suspect the tetras had ammonia burns, not fin rot.
Keep up with the water changes daily until you get a 0 reading for ammonia. Make sure you siphon the substrate well when you do this as you will be sucking up whitespot cysts too.
Increase the temperature, as suggested, and use the whitespot treatment as per instructions on the bottle.
It takes a while for all the signs of whitespot to disappear so don't disheartened.
(Don't panic at the water colour when you add the treatment either!)