M.Tech

Yes, you can take admission in BHU, Varanasi for this course.

It depends on your own interest. You can go for M.Tech in production and design.

You can go for MBA and you will find better options further.

Hi
You can pursue B.Tech immediately after your completing your 12th and giving the common entrance test for admissions. As Mr. Sunil Soni said, BE and B.Tech is the same degree. It depends on the college you select. You can apply to the various colleges like:
1. BITS, Pilani
2. IIT's
3. UPES, Dehradun
4. Vellore institute of technology, Tamil Nadu

Dear Pravesh Kumar,
For MBA admission, they need GMAT and TOEFL. For M.Tech, GRE or TOEFL scores are required along with the sponsorship letters.
All the best.

Yes, you can do both the things simultaneously.

MBA and M.Tech both are completely different subjects so you must clarify first that about which course you want to get the information.
But based on your question, I will suggest you 3 preferable countries for both MBA and M.Tech:
USA, Australia ,Canada and your country means India is also good but if you opt for India, you must choose the best institutes in India for it.

In order to work as an IT professional, you need to pursue B.Tech in CSE or MCA. Those who want to go in the teaching line or didn't pursue CSE in UG should opt for M.Tech in CSE.