Exploring the Legality of COVID-19 Vaccine Mandates

Q: Can employers, colleges and universities require COVID-19 vaccinations?

A: Generally, they may require immunizations. But there is some uncertainty about the legality of mandating vaccines authorized for emergency use by the U.S. Food and Drug Administration.
FULL QUESTION
Does federal law prohibit employers and other institutions from requiring the COVID-19 vaccine?
FULL ANSWER
According to a list maintained by The Chronicle of Higher Education,