M.Tech

Hi Jay,
This is a difficult question to answer. There are thousands of universities abroad and also you must be more specific about the country choice as to the university which will give you the admission will entirely depend on your overall application profile and the university's selection process. If you are planning for US, getting into a top university with 301 score in GRE will be tough. It is important that you first decide the country, start visiting university's websites across popular countries and check the requirements and shortlist accordingly.

Mechanical Engineering is the evergreen core branch of engineering. Job market for mechanical engineering graduates is stable for last 6 decades. If you are planning to do engineering then B.Tech mechanical is a good option. Once you complete B.Tech mechanical engineering, you may opt for M.Tech if you want to specialise.

B.Tech is a graduation degree and M.Tech is a Master's course.

You can write GATE exam and score a good percentile, you can apply for PSUs like IOCL, BEL and HPCL. Generally, they call top 500 rankers in GATE for PI. You can also go abroad for MS through GRE or TOFEL.

Yes, BITS organize different exam for ME or M.Tech. You can also take direct admission in some private institutions for ME or M.Tech.

no u can also proceed without gate.

It depends on your personal choice and aptitude, if you have aptitude and interest towards technical side, then I would recommend M.Tech. Otherwise, if management and non-technical field interests you, then MBA should be your choice. Both, MBA and M.Tech comes with its own set of pros and cons.