MAH CET

Just go through this link and fill out the required details:
https://www.shiksha.com/college-predictor

Hi,
Candidates must obtain Graduation degree in any discipline from a recognised institute with minimum 50 percent marks in aggregate (45 percent for reserved category candidates). All JBIMS applicants should have a valid score of at least one examination, namely. MAH CET/CAT/CMAT/XAT/MAT.

No, NEET is for the medical courses whereas to get to management you need to appear for exams such as CAT XAT NMAT TISS, IIFT etc.

Yes, Non-Maharashtra residents can appear for MHT CET. And also one (non Maharashtra resident) can secure admission without appearing for CET. 15 % all India (excluding Maharashtra) candidates.

Cut-off for MH-CET is 97+ for Gujarat quota:
https://www.shiksha.com/mba/course/post-graduate-diploma-in-management-k-j-somaiya-institute-of-management-studies-and-research-ghatkopar-east-Mumbai-11644.

Kohinoor, Rustomjee, Viva and Raheja are some colleges you can expect for MS For PGDM, you can choose Durgadevi Saraf which is better than a lot above mentioned colleges.

For PGDM, chances are good, but for MS cut-off is way higher. For details about colleges list and eligibility check the below-mentioned link:
https://www.shiksha.com/mba/exams/mah-cet.

Yes, you can get admission in colleges like Viva and Jamia Milia for MS Alternatively, go for PGDM as you can definitely get decent college with this score. Some options are NL Dalmia, MET IES and Chetana.

He chances are moderate. You can check the below mentioned link:
https://www.shiksha.com/mba/course/master-of-management-studies-xavier-institute-of-management-and-research-ximr-fort-Mumbai-113330.

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.