The mushrooms are simply an indication that there is organic matter in the soil that is breaking down. The mushrooms feed on the organic matter, and form fruiting structures when conditions are moist. As it dries out this summer, the fruiting structures of the mushrooms will go away. In the meantime, if you'd like to break them off with a rake you can do so. There is no effective fungicide to get rid of them.
Similarly, ants in the lawn usually cause no damage to the lawn, so they don't need to be controlled. If you'd like, you can apply ant killer directly to their mounds, but keep in mind that doing so will kill beneficial insects as well.