Colleges in Mumbai

IIT, Mumbai is the best college to pursue mechanical engineering.

IIT, Mumbai is the best option.

According to me, it is from CET but I will suggest you to prepare for JEE because the news is that CET is going to be cancelled for all engineering and medical students. If you will prepare for JEE and then there will be CET, it will not be difficult for you because JEE has little higher level then CET.
All the best.

Yes, you can definitely change college after getting O grade in FYBMM. You can apply for some of the good colleges like MMK, Mithibai, NM college of commerce and economics, National college, provided if you stay in Mumbai . You can apply for any of the good colleges in SYBMM. Rest is up to your choice whether you want to continue in the same college or some other college.

The admission process for the 2016-18 academic year was conducted through DTE and under that process 15% seats were given to all India candidates. CMAT is one of the exam considered for All India seats. Other exams considered were MHCET, CAT,XAT,and MAT . You can give any of the mentioned exams to be eligible to apply for those seats. Typically the cut off is 99.99 percentile.

You can check this on the website of IIT Bombay.

No B School can ever guarantee 100% placement. Bombay has 7 B-Schools which are in first 30 ranked MBA colleges in India. You may refer to link https://www.shiksha.com/mba/ranking/top-mba-colleges-mumbai-all/2-0-0-10224-0 for further details. If you do MBA from these colleges, you have very high chances to get a very good job and jump start to an excellent corporate career.

Hello Asif Raza,
It depends on you, but I will suggest you should opt for mechanical engineering because it is an evergreen field. Aeronautical also has a good scope, but it doesn't have much demand as compared to mechanical engineering. Mechanical engineering has more scope for future. In future, you can move opt for Masters in aeronautical engineering.