Mushrooms, or toadstools, are usually caused by decaying organic debris, such as pieces of wood and dead tree roots, just below the surface of the lawn; they can also be caused by a thick layer of thatch (the layer of grass clippings, dead roots etc that accumulate on the surface, just below the grass line - see here), and they thrive in damp conditions.
Given that there aren't many of them, and they don't seem to be the type that forms rings that grow wider and wider every year, I don't think you should be too worried; you may find them a bit unsightly, but they are not likely to cause much damage. If you're concerned about the 8-10" circle, you could lift that small piece of turf, remove whatever decaying matter is underneath, and replace it.
As far as I'm aware, there is no reliable water-on technique for ridding a lawn of toadstools; you could try iron sulphate (1/2oz in a gallon of water per square yard), but it doesn't always work and, when it does, sooner or later, the mushrooms often return. A thorough dethatching (or'scarifying'), on the other hand, might well do the trick - see Thatch Control here.
There is a good article about toadstools/ mushrooms in lawns here.