India

I am assuming you belong to open category.
Admission in top 5 colleges of Pune - COEP, PICT, VIT, MIT and PCCOE is almost impossible.
You may have a chance in colleges ranked below these.

Yes, there are some colleges in which you can take admission:
Central Institute of Plastics Engineering and Technology
Tamil Nadu College of Engineering
Government College of Engineering
Coimbatore Institute of Technology
St Joseph College Of Engineering, Chennai

No, it's not true. You should analyse both as if you don't have interest in any branch. Eventually, you will not perform the best in it.

Proposed combination can of any value in career if MBA is done from one of the top 100 International B-Schools and also you are able to gain international job experience after MBA. With increased restrictions on work visa for foreigners, your plan may have big challenges. Therefore, it is suggested

I will suggest you to take a short-term course in Canada related to your field. While studying you will be allowed to work about 20 hours a week. After the course you can target getting full time employment.

Hello Aman,
It's nice to know your intention of acquiring degree. In Maharashtra the best college for this is of course COEP, Pune. But there are good colleges in almost every district of Maharashtra. You should select that is most convenient.

Nowadays, most of the countries have started putting lots of restrictions on work visa for foreigners because of global economic slowdown. Therefore, there is no guarantee that you will get job after MBA from a International B-School and even if you get job will you get work visa. You will face lots