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You need to show best of 5, but the ultimate decision is made on the basis of your entrance exam.

Only engineering graduates are eligible for MBA in IITs and that is of 4 years.

If you want to get enrolled in IIM first you have to crack CAT (Common Admission Test).

No, you can't. According to 2016 cut offs of AIT, Pune for CSE branch is 68239.
According to JEE Mains marks vs rank, to get this rank you need to score 130-140 at least. But cut offs varies every year. So do as much as you can.

Hi Aghil, UK has some of the very famous business schools like London Business School, LSE, Imperial College London, University of Cambridge, University of Oxford, Warwick Business School, University of Bath, Cardiff University, etc. You can check the business school websites and read about the class profiles to have an idea about the student preferences. Prepare accordingly.

Hi,
Placements (in INR; as provided by college)
Minimum Salary (Annual): 3.00 Lakh
Median Salary (Annual): 4.96 Lakh
Average Salary (Annual): 4.96 Lakh
Maximum Salary (Annual): 7.00 Lakh
Companies where students got placed
Attune Technologies ColumbiaAsia Deloitte Global Hospitals Insta Healthcare solution Pvt Ltd NRHM Gujarat
https://www.shiksha.com/mba/course/post-graduate-diploma-in-hospital-and-health-management-institute-of-health-management-research-electronic-city-bangalore-277900