Exam

It is possible, but your class 12th marks should be very good. I mean you should be in top 5 from your state.

Yes, surly you can get, but I dint think it would be a core branch.

You can take admission in around 111 colleges under Gujarat Technological University (GTU), by simply applying to ACPC following by counseling, but from this year GTU started considering their own exam named GUJCET, therefore the seats are going to be distributed between GUJCET and JEE, also there a

If you don't have 75% marks in board exam, then you are eligible.

For CSE you should atleast have around 300 marks.

Yes, you can apply for one more entrance exam for engineering, and if you want to pursue B.Tech from Mumbai, then you have to qualifying MHCET entrance exam for same.

BA College of Engineering & Technology
Birla Institute of Technology, Mesra
NIT Jamshedpur
Guru Gobind Singh Educational Society's Technical Campus
University college of engineering and technology
Cambridge Institute of Technology

If you belong to general category then 400-500 is ideal.