After most showering and toilet flushing, there is a loud hum/ vibration that comes from the water system. It sounds like an air lock or something. We have city sewer and water. Any ideas on how to get rid of this noise? Does it do any damage?

Check the toilet tanks. It sounds like a vibrating washer. Check the tank water level, it should be at the mark in the tank or 3/8 to 1/2" below the top of the over flow tube. Now look at the flapper, If it has wavey edges on the flat surface, replace it. The linkage between the flapper and the flush lever should have 1/4" play when the tank is filled. Also, check the small tube coming out of the top of the bakkcock and make sure it's connect to and draining into the white overflow tube. More questions? I'm as close as a click. TOM