International Business

Yes. It's possible.

Yes, based on your category, you can get admission in MBA international business.

Top UK Universities to Study International Business
The University of Warwick. The University of Leeds. The University of Birmingham. The University of York. London School of Economics. The University of Manchester. The Queen Mary University of London. The University of Kent. You may pursue an undergraduate degree from all of the colleges above but you will need an English entrance exam Like IELTS for it. Each university has a different score requirement for the course.

For the latest cut off go through this link.
https://www.shiksha.com/mba/iift-exam-cutoff

Please specify the college you are asking about.

Course Cut off range-
BA Hons. (Arabic) 64.25 - 90.75
BA Hons (English) 48 - 67
BA Hons (Economics) 48.50 -70.75
BA Hons (Political Science, Sociology, Psychology) 60.25 - 70

Yes, they offer BBA INTERNATIONAL BUSINESS

May be good but not best. IIMs are the best for 5 years integrated Programme in Management courses after 12th. IIMs will provide you best scholarship and loaning facilities if get selected there. So prepare yourself for IPMAT entrance exam.
For more details, please visit https://www.iimidr.ac.in/academic-programmes/five-year-integrated-programme-in-management-ipm/

I would say you should go for MBA in International Business as it provides you a corporate practical experience of how things are done and the approach is very professional where as M.A. might have a theoretical approach towards the curriculum.

The courses include B.A. (Hons) - International Business &a Finance,. Indian School of Commerce, Bangalore Courses and Fees 2022, refer to the link below-https://www.shiksha.com/college/isc-indian-school-of-commerce-bangalore-vasanth-nagar-63219.