MBA/PGDM

Are you talking about IMI Kolkata?

Yes, Diploma holders can apply, but only if you have a 3 or 4 years Bachelor's degree with minimum 50% as aggregate.

Yes, GMAT it is acceptable.

Hello, your IELTS score is too low for you to get into top ranked universities in Europe. You should score at least 6.5- 7 in your IELTS.

Hello, you can apply for MBA programme in sports management in USA. You will have to appear for GMAT exam and have 3-4 years of work experience.

On India level, you can find many colleges which have done remarkably well for students, but if you are limited to Jaipur then I suggest for UEM Jaipur. The website link here will provide you with best information on programs and admission process with placements for career opportunities https://www.shiksha.com/mba/course/masters-of-business-administration-university-of-engineering-and-management-jaipur-236845.

If you intend to mention Pune Institute, B S Dhole Patil Path, is a private college and does not have affiliation form Kalinga University. It does not offer MBA in quality management.
https://www.shiksha.com/college/pune-institute-b-s-dhole-patil-path-36992/courses?uaf[]=base_course&ts=86272173&rf=filters&bc[]=101

Please go through with the UEM Jaipur college link https://www.shiksha.com/mba/course/masters-of-business-administration-university-of-engineering-and-management-jaipur-236845 and you can even download the placement report for closer look at the performance of the college in respect to MBA.

As you are aware of some good colleges in Jaipur, I suggest for UEM Jaipur which is also the most competitive college among them and will help you to find the best placement possibility. The link of the website from here will definitely give a rough idea of the college https://www.shiksha.com/mba/course/masters-of-business-administration-university-of-engineering-and-management-jaipur-236845.