All these things that you have mentioned here matters a lot for a student to get admission in any top most B-School in India. But, apart from it the thing which matters the most is how you present yourself at the time of GD (Group Discussion) & PI (Personal Interview).
Since, you have MAT scores, first find out the cut-off marks of the colleges you wish to apply at and make a list of the colleges you are eligible. Then, you can do an assessment of which college is the best of the lot.
Click here to get the list of management colleges in India
You can compare colleges as per your preferences by using our Compare College Tool.
All the best !!