Maharashtra

At this score you can look for colleges like Loyola Business School, Alliance, Amity, SIESCOM-Mumbai, JIMS-Rohihi, Jaipuria Institute-Lucknow, IPE-Hyderabad, ITM-Navi Mumbai, XIME-Bangalore, KSOM-Bhubaneswar are some of the institutes you can consider.

Talking about Pune, you can try for SIBM, SCMHRD by clearing SNAP and then GD/PI rounds or PUMBA by giving CET/CMAT/CAT and then via CAP process of DTE Maharashtra.

Do it from Symbiosis, Pune for better learning and placement.

Yes of course you are eligible for admission in ITM Navi Mumbai. 122 is a good score and you'll definitely get admission in this college.

Yes, you can and you can get an lateral entry in second year.

Hi, List of colleges with your score:
Acharya Bangalore Business School (ABBS), Bangalore
Asia Pacific Institute of Management, New Delhi
Jaipuria Institute of Management, Noida
IFIM Business School, Bangalore
Prin. LN Welingkar Institute of Management Development and Research, Mumbai
Birla Institute of Technology, Mesra, Ranchi
Dr. D. Y. Patil Vidyapeeth, Pune
Prin. LN Welingkar Institute of Management Development and Research, Bangalore.

Hi, You can refer the below list of colleges:
ITS Institute of Management, Greater Noida
Vignana Jyothi Institute of Management, Hyderabad
Galgotias Business School, Greater Noida
BIMTECH Greater Noida
https://www.shiksha.com/mba/colleges/mba-colleges-accepting-cmat-india.