Colleges in Mumbai

Mohini,
As per your score, you can look for:
Lovely Professional University, Delhi
Xavier Institute of Management and Entrepreneurship, (XIME Bangalore)
Universal Business School, Sion, Mumbai
Indus Business School, IIEBM, Wakad, Pune
Christ University Institute of Management, Hosur Road, Bangalore

The chances to get IIT Bombay seems low whereas IIT Madras is very high if you perform well in GD/PI. Last year the cut off for Bombay was 90%+ whereas for chennai was 85%+.
Also if you want,you can consider IIT Roorke and IIT kanpur. Chances seems good in these IITs also.

The profile-cum-score short list have been released. The selection depends on parameters which are academic and non academic. A profile which has versatility is also appreciated.

Along with SPJIMR, NITIE also offers specialized courses in operations

For the interview you cannot change the specialization. Change of specialization is possible after first year owing to certain guidelines. But the specialization you have been called for is based on the preferences you have given and your profile.

Yes you can get into jbims.snap is not needed instead you need to give cet for admission in jbims.

Yes, you have an excellent chance of getting GDPI call from SIMSR for the PGDM program. SIMSREE, as far as i know, does not have PGDM, but a representative from that college will be in a better position to answer.