GATE

Do your course subjects really well. Watch NPTEL videos. Just try to understand your core subjects deeply. If books are not sufficient then go for video lectures. And when you are done with this, go for practice papers for GATE to get idea. Give yourself tests to get into time management thing.
Good luck!

Yes, there are many colleges in Mumbai who get the admission by this score, you can check online according to your branch preferences in M.Tech or you got call from different colleges for M.Tech.

Brother, coaching institutes are just making money. The best tutor is within you. Do self-preparation because self-study is the best study. No one can teach you as you can to your own self. I too am from same department (aerospace) and could see you as a mate. Stop thinking about joining a coaching institute and clear it by yourself. Have a nice day!

GATE is difficult. Don't compare these two exams.

Industry likes one should be engaged either in a job or continuing with learning. A management programme is appropriate for you.

You may refer to following Shiksha link for tips on GATE preparations:
https://www.shiksha.com/engineering/exams/gate/preparation-tips

You would be eligible through GATE score and not CAT.

Made Easy is the best coaching centre in India for the preparation GATE exam.