What kind of water should I use for a terrestrial salamander to spray the habitat and put in the water dish?
You can use tap water, treated to remove chlorine/chloramine as explained above. Or you can use bottled spring water. If the animal is not going to sit in the water much (or if the water is only used to spray the habitat), distilled or RO water may be used. Distilled or RO water will cause less residue to accumulate on the glass, as compared to tap or spring water, which contain some minerals.
