What is based on the fact that oil and water don't mix?
Of the two paints you are going to try mixing, a water based paint (latex), with a spirit based (possibly methalated) . Not a good idea as they will separate. DO NOT MIX! On the containers for these paints you will be told how to wash your brushes ie.. Water for Latex. Turpintine, or Varsol for the Oil based paints and stains. Again, Oil and Water do NOT MIX!!!
NO, that's messy. Take a small stick, scoop some paint into a paper cup and mix it with water, -if it mixes easily it's water based. If oil based it won't mix at all. If you're checking dry paint, put some denatured alcohol on a rag and rub the surface. If it comes off on your rag, it's water based. If all it does is clean the surface, then it's an oil.
Most solid color stains are water-based, and most semi-transparent stains are oil-based - therefore, you cannot mix the two together for good results. If you are not sure which variety you have, check the label for "cleanup" instructions. Oil-based stains will require mineral spirits for cleanup. Water-based stains require soap and water only.