Is this legal?
Sure is. No law protects management from having to sully themselves with grunt work, neither does the law protect them from having to work longer hours.

May I quit my job and apply for EDD while looking for a part time job and go back to school?
No. Quitting for no compelling reason disqualifies you from drawing UI. ("I can't take it anymore!" is not a good enough reason.) Attending school disqualifies you from drawing UI because it renders you unavailable to accept full time work.