Our experts are on leave so you will have to settle for my intuition.
PS fluid and ATF are not soluble in each other, so who knows what proportion you have and what properties the mix has. You can get along with your wife and with your girlfriend, but they do not mix well. To flush the system at home you can siphon out the fluid and put new ATF in, repeat a number of times until the old stuff is really diluted. I have done that with a syringe on my E24, but it is very important not to re-use the syringe for food or medicine. My wife uses a a syringe for decorating cakes. People stopped coming to our parties after I re-used it.
Maybe find the leak first. I hear there is a trace fluid that will show where the leak is, I envision neon colored ATF and the leak will show a neon color streak. Ask a friend at the airport to run the car by the TSA machines that show you naked, the leak will probably show right away. Make sure you are not in the car. Stan would eventually upload to the registry the picture of a naked guy in a coupe at the airport and will rat you by the VIN number.
Do not operate the pump until you refill with fluid. You can bleed the system to remove air bubbles. Turn the steering wheel a few times and top off after air bubbles come out.
Caveat Emptor. This is advise from a person that never did this, and on a foul mood day. I should flush my spleen and put ATF, maybe I would be a nicer person then.