You can't calibrate a pH meter with distilled water, unless you know what the pH of the water is of course. Its most likely not pH 7, or even close enough to 7 to calibrate. What you want is a calibration solution.
All good then. You could probably get away with tap water to rinse, otherwise H2GO or Pump (RO water) should do the trick. I think Pure Dew brand water is distilled?
pH of distilled water can fluctuate due to dissolved gases eg CO2. The value can fluctuate quite a lot as there are no other ions to buffer out.
For the refractometer you need to recalibrate on each day you use it, and often through the day too. (why it drifts I do not know). I just take a little sample of the steam that condenses in the lid of the electric kettle (the one used for making cups of tea that is!) each time for this purpose. You only need a tiny tiny drop.
For the pH meter I just rinse with tap water before calibrating with the pH 7 solution. The pH target of 5.2 isn't critical as far as I understand, talking to a commercial brewer here he told me he just makes sure it is somewhere 5.2 - 5.4 or even 5.6 through the process, so you don't need 5.200 precision...
You get distilled water out of a steam water purifier or any still.
How about rain water?
I wouldn't trust any gas station, mitre 10, supercheap, repco etc...they usually get the water out of the tap!