Sports

Yes, you can become the student of IMS as it accepts CAT score as well.

Some of the best sports management colleges in India are:
1. Osmania University - Hyderabad.
2. Guru Nanak Dev University - Amritsar.
3. University of Mysore.
4. University of Madras - Chennai.
5. George College - Kolkata.
6. University of Calcutta - Kolkata.
7. Jiwaji College - Gwalior.
8. Tripura College - Anjaw.
9. Meenakshi University - Chennai.
10. Karnataka University - Dharwad.
I hope this helps.

You don't need any course to pursue BE. The career prospects are very good for computer science especially into app developers, coding and business analytics, software testing and presales and consulting.

You can pursue PG Diploma in sports psychology through distance in Mumbai University.

First, you need to decide which career do you want in cricket? Do you want to be a cricketer, a cricket commentator or a cricket journalist?
In terms of other sports, it would be great if you decide your area of interest and in which you wish to make your career and then take the coaching for the same to train yourself and take a platform to perform. Eventually, if you become good in that specific sport, then you may have a lot of options further.

Join a cricket academy, and play well. Try out for some club selection and show them what you have got. Give trials for state selections and zonal level cricket competitions, and then you may have the chance to play Ranji. Slowly, you will get better and can play international cricket.
Note: Age doesn't matter.
Abhimanyu Mithun (Indian cricket bowling ace) started his career at the age of 17 and played international cricket at the age of 20.

You need to opt for physical education subject in class 12th.

Sports manager and multimedia is a different field. For sports, you can do some Diploma courses in cricket. Also, there is some standard degree like: BPed or CPed.