Read the instructions on your nutrients. If they do not mention PH'ing your water after adding nutrients than it would be safe to say to check the pH after the nutrients have been added.
pH = Acid/Alkaline balance of any given mixture/liquid
ppm = parts per million
tds = total dissolved solids (another way to say PPM)
ec = electrical conductivity (another way to measure the TDS/PPM)
It seems as though you already had a grip on what pH was, but basically the last 3 are all different ways to measure the same thing -- How much nutrient/additives are in your water. I usually just stick to reading by PPM. It's the most commonly used and accepted method of measurement.
You don't need anything to make sure you flushed well. If you are in soil, you need 3 gallons of water for every gallon of soil, and if you are in Coco Coir you will need 2 gallons of water for every gallon of soil to ensure a proper flush.