My bathroom sink issues

My bathroom sink has been leaking water on the floor and also has a large crack in the white part where the water runs. Not sure if that is causing water to pour on the floor when I brush my teeth, etc. Also I randomly have my bathroom sink and my tub stop up too and I used Crystal Heat on both which cleared that up but underneath my sink is always soaking wet and I am concerned about mold. Does this sound like a problem with the bathroom sink or with the plumbing underneath my house? If it's my sink, can I somehow replace that white sink part or am I going to have to get a whole new sink installed?