If they are real mushrooms,they pop up only during rainy season.Try to keep the soil dry.They won't do any harm to you.But some are edible.Use them for meals.Otherwise plug them away when ever you see them.You can use pesticides and Clean daily.
stop watering so much, if you are not watering the problem will go away once the soil dries out and the dead organic material is consumed. You need more sun in your yard its too damp and thayll keep comeing back
I have found that if you wait long enough, winter comes. I am not sure if they are actually gone, but you can't see them below the snow. I really do not know about fairy rings, I think they are against the law here.