Indian Institute of Technology, IIT Bombay

No,
In order to get admission in any of the IITs, you need to appear for JEE Mains and JEE advanced with less than 100 AIR to take to admission in CSE in IIT Bombay.
With the present 12th marks, you are not eligible to take admission in NITs.

You have to get top rank in JEE Advanced and by choosing the option in counselling conducted by JoSSA you may get seat in IIT Bombay. All the best.

If you want to pursue M.Tech in IIT Bombay then it does not depend, which was your earlier college you did B.Tech from. You can do both the degree programmes from different colleges.

Hello Bhargavi,
As far as I know, the only way to get admission for M. Tech admission at IITs is to clear GATE with a good score. If you haven't attended the exam, then it is impossible to get a seat.

If you want to pursue engineering then you have to study maths or science in your 11th. You should opt for maths. Good luck.

Indian Institute of Technology (IIT) Bombay announces admission to Ph.D programme 2019 (Spring Semester) IIT Bombay Ph.D. Admission 2019. Indian Institute of Technology (IIT) Bombay invites applications for admission to the Ph.D. programs for the spring semester of the academic year 2019-21.

Yes, if you will get more than 8.5 GPA, then you can.

You need to appear in special exam and interviews for the same. Based on your performance in the exam and interview, you will be given a seat in IIT Bombay. So, admission will be merit basis only.
Best of luck.

In B.Des, there is no specialisation offered. It's a simple B.Des.