M.S

Hi,
It is IELTS for English language proficiency. No other tests are required unless a university specifies it. You have to be very good academically and an IELTS of more than 7 is recommended.

Hi Kunal,
A GRE score of 315 and above is strongly recommended.

Admissions are based on GPA, Letters of Recommendations from your professors, GRE scores, personal statements and any work experience/projects. TOEFL is used only as a proof of English proficiency and doesn't really matter for admissions as long as you're scores are above the cut-off scores. Since really bright/really nerdy students apply to MIT MS, I think you'll need a CGPA of 9. If these 5 parts of your application are stellar, I don't think you need to worry about the "prestige" of your engineering college.

BKSBM is the most preferable. But you can choose as per your convenience. Also, you should check the specializations they are offering.

No, you can't get CSE as you have done B.Tech in ECE. You can only get ECE branch or any other specialization.

Yes, you do. Here are the requirements:
https://www.qut.edu.au/study/international-courses/master-of-project-management