Why would the water and everything come out of the downstairs toilet when you flush the upstairs toilet?

Answer The waste line from the downstairs toilet is not vented (or not vented properly, or the vent is plugged up). Flushing the upstairs toilet creates a vacuum in the main line which sucks the water out of the one downstairs. Answer your waste lines for both toilets may be on the same branch off the sewer main. Either you have a stoppage in the branch line or you have a stoppage in the main line. (If it's the main line your downstairs toilet would have to be the lowest fixture, ie If you have a floor drain downstairs and it's a stoppage in your main line it would backup through the floor drain. If there is no floor drain the toilet downstairs is probably your lowest fixture.) Your best bet is to snake out the system through the toilet downstairs.