B.A

Based on your educational qualifications, it is recommended that you may opt for marketing or HR specialisation in MBA. Both specialization have good job and growth opportunities.

BA and B.Sc are different fields. If you opt for B.Sc, you will be placed in the scientific cum technical field. After BA, you would have to pursue arts as a career. If you want to appear for civil services, either of the two should suffice. You should opt for the course you are comfortable with and where your interests lie.

Go to your college administrative office and ask what you need to do to BA (Pass). They might ask you to pay some fines and take the exams or they might ask you to complete the same next year.
If you don't want to finish BA at all then join some other course.

There are no good universities that will give you admission with such a low percentage. Kindly tell us about your location, so that we can suggest you some institutes near your location.

ICFAI, Hyderabad is the best campus among all the campuses of ICFAI. The average placement package is 6-10 LPA.

Yes you can. Any graduate with 50% marks can apply for MBA.

Yes, you are eligible. But you must score 50% marks in your graduation.

Although, you want to pursue your BA in distance, you don't join any state open university. You only take the BA course from IGNOU, Chennai regional centre in distance because it is world's largest open university and its degree is valid worldwide for higher education.