IIM Indore - Indian Institute of Management

Yes, international opportunities into summer's internship have been offered over years as well as student exchange programme is offered. XLRI is more recommended for international internship.

TIME, CPLC are the best coaching institutes for CAT and all other entrance exam preparation, following by GDPI preparation which is very important.

Refer Shiksha website for your question:
https://www.shiksha.com/mba/exam/cat

It depends a lot on the college. For eg. MBA from an IIM will clearly hold more value. In addition to that, MBA is a more widely recognised course.

Get a clear idea of what the syllabus is. I hope you know that the exam consists of Quant, LR/DI, and English. Start practising. There are a lot of books available. Give time to all the four and to get an idea of the difficulty level of each, solve the previous years CAT questions. You can choose to take the test series of any coaching institute, later, if you think you need it.

You'll have to take CAT. That is a prerequisite.

Score at least 95%ile and above.

The higher your score, the better your chances. Aim for 95 above. Nothing can be guaranteed as of now. Different IIM's have different cutoffs. They also vary every year.

IIM - Indore does not offer BBA course. It offers 5 years integrated program in management.