Could I go to a school like Pima Medical Institute while unemployed without loosing unemployment benefits?

I think the only way you could is if you were still actively seeking work. Also available to work if you found a job. In some states they will pay for you to be retrained if the company you worked for went out or business. If you haven't already ask some one at your local labor board make sure they are aware that you will still actively be seeking work and will take the job if you were to find one.