Ones who buy medical indurance through college, does that cover dental emergencies as well or do you buy dental insurance separately?
Dental insurance is almost always separate from health insurance. Health insurance would cover an injury to the mouth (hit with a baseball, fall and crack teeth) but not the repair by a dentist. It is up to state law if dental coverage is required. Most states do not require it, especially for adults.
Long ago my kids had private Blue Cross policies and the state of Colorado required dental insurance on policies for children, so they got 2 free cleanings per year and some other limited coverage. That was before ACA so those policies aren’t available any longer.