Washing machine running water coming out of toilet

I noticed that my toilet has started bubling. The washing machine was running. I happened to noticed that the toilet in my spare bathroom had water coming out from under the toilet. The tub beside it looks as of at one point dirty water had possibly backed up in it (I don't use the tub, I could...

When I flush the toilet, take showers in my upstairs bathroom, water comes out of my downstairs shower. How can I fix this problem without calling a professional plumber?

The cold water dribbles into the washing machine when loading; I checked hose connecting machine to faucet in back. The screens were dirty; every time I do load the screens get dirty again. Is stuff coming out of the faucet? It seems to me. What does that mean? The hot water faucet is fine. My...