MAT

Hello,
Yes, you can pursue either of these degrees since they would add more weight age to your credentials. Pursue it only from a good college though. Good luck.
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india/2-2-0-0-0

Yes, you are eligible for second stage.

Christ has a cut-off with more than 600+ marks jn MAT you can alternatively choose PSG Coimbatore and IBA Bangalore which are decent enough.

1. Mission MBA guide by BS Sijwali and Tarun Goal by Arihant.
2. MAT entrance exam with practice CD by GKP The Pearson.
3. MAT super course with CD by Pearson Study package for MAT by Arun Sharma.
4. 10 challengers MAT 10 mock tests for MAT by Dharmendra Mittal.
5. MAT score accelerator by Odisha publications.
6. MAT solved papers by Odisha experts.
7. 10 mock test papers for MAT by Career Launchers.
8. Barrons guide for MAT by Eugene D Jaffe.
9. MAT entrance guide by Deepak Aggarwal.

You need to apply for PGDM, dates must be over by this time, you should contact the colleges for further information. https://www.shiksha.com/mba/course/masters-of-management-studies-st-francis-institute-of-management-research-sfimar-borivali-west-mumbai-110812.

MH-CET, chance is good enough. For MAT you need minimum 90 percentile. https://www.shiksha.com/mba/course/master-of-business-administration-mit-school-of-management-mitsom-kothrud-pune-2340.

For MS course, you can choose Indira-Pune, Durgadevi Saraf, Alkesh Dinesh Modi, Vidyalankar and Don Bosco. For MAT scores compare your score with cutoffs of different colleges mentioned below and choose accordingly:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india-accepting-mat/2-2-0-0-306.

MAT cut-offs listed in brackets as per the composite score is given below for all colleges. https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india-accepting-mat/2-2-0-0-306.

They don't accept MAT for admissions and eligibility see below. https://www.shiksha.com/mba/course/master-of-business-administration-jamia-millia-islamia-jamia-nagar-delhi-190341.

Below colleges are good choice with high probability at this score. https://www.shiksha.com/mba/ranking/top-mba-colleges-in-bangalore-accepting-mat/2-2-0-278-306.