Is it compulsory to have work experience for admission in MBA colleges? If I am a fresher, will I be eligible to enroll?

No, its not necessary to have work experience for doing MBA. But there are some best colleges like IIMs who gave weightage to work experience for admission.

No, MBA can be done without having to work. But internship is very crucial in the business studies.

You need to have scored 50% marks at your graduation level and based on your score in entrance test like CAT admissions are given. At the time campus placement post your MBA prior experience does carry a lot of weightage.