M.Tech

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.

No, NICMAR - Pune does not offer this course. They are offering Post Graduate Programme in Construction Management (PGP CM).

If you want to acquire thorough technical and practical knowledge of a subject, then opt for M.Tech otherwise, opt for M.Sc. M.Sc has more focus on theory than the practical aspect of a subject. Choose your stream as per the nature of the job you want to get.

Apart from IITs (Kanpur, Roorkee and Guwahati), NIT Warnagal, NSIT Delhi, Thapar University, Manipal Institute of Technology, Karnataka, Vellore Institute of Technology (VIT); and Sir M. Visvesvaraya Institute of Technology, you may check at the following link:
https://www.shiksha.com/top-bio-technology-colleges-in-india-rankingpage-54-2-0-0-0