I'm not an expert - can only base my advice on my own experience.
I would think fresh water will help heal your little guy's tail.
I would suggest keeping the water pristine - with nitrates definitely below 40.
I don't think warm water will be helping if not ich, and may be compromising the quality of the water.
Hope this helps.
I agree as well. A nitrate level of 40-80ppm is quite high and likely a primary factor contributing to his fin issues. Healthy water along with an appropriate diet can do wonders for fish health. Rather than topping off with distilled, simply increase the size and frequency of your water changes and make sure he is eating a nutritious diet. Keeping your nitrate levels below 20ppm (preferably, below 10ppm) should help along with diet.
The white spot that you saw on his wen was just part of normal wen growth- expect to see white 'spots' on his wen more frequently as he matures. This is perfectly normal but its also important to keep your parameters in check during these growth periods to limit any possible risk of infection. Please ask if you have any questions!