If I apply to a college and get accepted can I change my VISA to a F1 and can I apply for a work permit with a F1 VISA?

No, you are not permitted to work while in F-1 status except on very limited basis, on campus.

If you get accepted to a college that is authorized to enroll foreign students, the college will issue SEVIS forms that you need to change your status to F1. As a general rule, F1 students do not get work authorization; and by accepting unauthorized employment, you will violate your F1 status and give USCIS reason to cancel your visa and ask you to leave the U.S. As part of the application to change your status to an F1, you will have to show that you have money to pay for your studies and to live in the U.S. - or have a sponsor who will take care of your needs here.

Yes. If you are still in valid immigration status and have been accepted to a school, you can apply for a change of status from B1/B2 to F-1. The application is submitted on form I-539 along with your I-20 and evidence of sufficient funds to pay for tuition.