Mumbai

Any IT recruiter looks for following in any B.Tech IT student during campus placement: Analytical and Creative thinking, Masterly on at least one Object Oriented Programming language, strong Data structure and RDBMS understanding, Soft Skills, willingness to learn ( this is tested by your knowledge on latest in the field of IT) and general awareness. If you work hard on your academics and participate in extra curricular activities to develop your personality, you will able to get a very good job.

Refer below mentioned link for details:
https://www.shiksha.com/engineering/colleges/b-tech-in-computer-science-engineering-colleges-mumbai-all

MCC in Chennai and NMIMS in Mumbai are the best colleges.
You can check best BBA colleges in India:
https://www.shiksha.com/top-10-bba-colleges-in-india-article-7797-1

There are some good colleges, accepting MAT scores in/around Mumbai. Some of them are:
ITM Business School, Kharghar.
Institute of Business Studies and Research, CBD Belapur.
Thakur Institute of Management Studies and Research, Kandivali.
Thadomal Shahani Centre for Management, Bandra.
Durgadevi Saraf Institute of Management Studies, Malad.
Vivekanand Education Society's Institute of Management Studies and Research, Chembur.

Well, its good for placements. Although, there is a very tough competition, since all the colleges are together for placements. If you have it in you, you'll surely get placed in a good company. Not only placements, teachers for some of the departments are very good.

This is the link where you can see all the colleges with rating and fee structure:
https://www.shiksha.com/mba/ranking/top-mba-colleges-mumbai-all-accepting-mat/2-0-0-10224-306.
Some college are listed below.

Yes, you can if you have a valid degree certificate, and your entrance exam scores match their cut-offs. Do once again confirm with admissions committee of the college, regarding your graduation criteria.