MBA Eligibility

This question can only be answered by the institutions or HRD of GOI.
Changes do happen in eligibility criteria, syllabus patterns etc.
So there might be some changes coming in the near future but nothing can be predicted.

For getting admission in MBA in FMS you don't need any experience but your CAT score.
Entrance score and then your Interviews and GD's score will matter if you want to get admission in MBA.
All the best.

No, there is no sports quota for management courses in DU.
As far as I know, admission will be purely on merit basis.

Amity university is a average university, one can get easily admission in Amity. So, don't worry. Course fee is much higher. Placement is substandard. So, try for other better institutions and last option should be Amity.

Cracking CAT and all other competitive exam is not that difficult but not that easy first prepare plan for what you want to do and how you will achieve it then start with the tasks related to the plan define priorities so preparation for CAT requires already 9 months if basic concepts are claw then 6 months including solving practice papers so do not worry, concentrate on what you have and then kick start for the new task.

You are eligible to seek admission in MBA under foreign national quota. Every university and B-Schools has its own admission process. You are advised to choose few colleges and then do research on Foreign national admission process.

You can refer the link:
https://www.shiksha.com/mba/colleges/mba-colleges-india?uaf[]=location&ts=8996845&rf=filters&ct[]=702&ed[]=et_20

First, appear for any of the competitive exams, like CAT or MAT. The IIMs, though say that a minimum of 50% is required throughout your academic career, they do give a lot of weightage to a far brighter academic record. However, other institutions are also available. But it all depends on how much you score in the entrance exams.