On the other side of things, I would think vaporizing water would tend to give you something more like fog without using Ignem. That works perfectly well for most purposes other than scalding or building steam engines, and the latter are a bit later in history.
5th edition has been trying to move away from the requisited that were so ubiquitous in the 4th edition.
And a good thing too, 4th ed was hell for an cold/ice magus, because of the need for both Aquam, Ignem and even Terram (because ice is a solid).
Rego is used to change water into ice or steam, because this is natural proces for water. Although it needs the presence or absence of heat for this, using magic can skip this step. However the ice IMHO is not hot, it is still cold but it will melt fairly quickly without using PeIg to keep it cool.
As for salt water, can it naturally turn to fresh water? I don't see this happening, thus by the water-ice analogy cleansing salt water is not a Re effect in this way. Altough I could see Rego being used to separate the salt from the water. And I could almost see it as T:Part because clearly is a distinct part from the water. But it isn't actually one part, it is actually maaaany small particles, so are we talking T:Group here? As for Form salt is a solid and should be covered by Terram. But could you instead move the water from the salt? Then the water would be an Ind?
- Yes people understood evaporation, and people understood boiling water- the point is not that they did not understand either of these things but rather that they did not understand these to be the same thing. From a medieval perspective boiling water requires heat while evaporating it does not, so they are likely not the same thing- if you ignore the scientific evidence we have compiled since then.
- Yes, salt water can be changed into fresh, through multiple mechanizations. The easiest is distillation. It is also changed from salt to Fresh by filtration, which happens in numerous locations where there is a water table which is the same as the sea level but the rock/sand filtration results in fresh water coming from the well which is basically filtered sea water. Salt can also be extracted by freezing, as the ice is always fresh water and can be relocated and then melted.
You could ReAq/Te the salt to solidify into a layer, a salt cake you might say, which would form at the bottom of the barrel and stay separate for the duration of the spell. The water layer may not be pure, in that there would still be unhealthful liquids mixed in, but it's not salty.
Pour off the fresher water for a boil, and you should be good to go.
to me it seems like simple craft magic- with a potential finesse roll for efficacy. It isn't like salty and fresh is a binary condition, there are degrees of salinity.