We really can't tell from your photos exactly what you have there. It does look possibly like a mold just growing on some sort of organic matter there. It doesn't look like anything that would be a hazard to your new plants. 

The area looks pretty damp or even wet with weeds that could spread and compete with your new flowers for water and nutrients. We'd suggest pulling the weeds and or covering them with no more than 2-3 inches of mulch. Keep the mulch pulled back from the stems and trunks of plants.

As far as mushrooms go, they just pop up when conditions are just right, normally when it is warm and moist. They are natural and generally harmless (though don't eat them). Many are decomposers which grow on wood or old roots beneath the ground, helping them return to the earth. If you don't like them you can just kick them over or shovel them into the trash. They cannot be prevented.

Christine