Doing things in space will be much different than doing things here on Earth. Purifying water or even metallic elements might only need a concentrated source of sunlight and a giant foil bag to contain the materials to be processed, and a magnetic coil to separate elements.
Controlling the amount of heat applied to the foil bag could allow very fine control of the purity of the elements being separated, and using the magnetic coil as a form of mass spectrometer could allow the escaping vapours or plasma (depending on how hot you run the thing) to be separated and condense on cold plates.
Since we are talking about water, separating water from brine should be rather easy using a variation of this method. Of course, you could also forego the separation and simply use the mirrors to "raise steam" and make a simple steam rocket. This should work well from Mars inwards (farther out and the mirrors will need to be improbably large; this will add a lot of mass and complications to the focusing and control of the device).
For some consideration on
where to go to, here is a blog about using the voids inside asteroids to create habitable spaces:
http://gravitationalballoon.blogspot.com.auLots of interesting speculations and worked examples.