I don't think you need to worry about your water too much. The e.coli are pathogenic organisms and should never be present in drinking water. That is why they test for it. Naegleria is an amoeba found in warm unchlorinated water like in pools and ponds. Bad stuff but not in chlorinated supplies. Most of the other stuff are salts. Yeast actually need them in small quantities and some people add gypsum and epsom salts to give them more magnesium or calcium. You have high hardness (calcium and magnesium) high alkalinity (lots of carbonates and bicarbonates) so that is why your pH is above 7 (slightly alkaline). This is why your mate cannot put fish in it. Softening will remove calcium and magnesium (which cause scaling in pipes) and replace with sodium. Not much benefit. The main thing you should do when fermenting is to adjust your pH by adding citric acid. Many recipes call for citric acid to lower the pH to 5.5 You may need to add a bit more than some people to get to this. Buy a pH meter.
You don't mention chlorine level but the yeast can handle small amounts. Otherwise pour your water the day before and let it sit or even aerate it a bit and the chlorine will dissipate.
None of the salts are going to distil over so not all that relevant for the ferment of distilled products. What you cut your spirit with is the important bit. Rain water is good.