B.Tech Scope

Yes, you must take GRE and TOEFL. Also be aware that there is no government college. They are known as public or state universities. Other than these, they have private universities. You may also not find M.Tech. The degree notation is MS. Best of Luck.

Agricultural engineers are employed by Agricultural equipment manufacturing companies, FMCG companies , Agricultural & it's ancillary, R&D, acedmics etc. Starting salary will be above Rs 25000 pm. It has good scope in India.

No. Its not a residential course, although hostel facility is available and i recommend you use it. Bus facility is also available. MBA after b.tech is your personal choice. Being a b.tech myself what i think about it, you are widening your opportunities doing PGDM after b.tech but it is hard too if you are looking for a technical job after MBA. And yes dual specialization is available in VJIM.

Its at least 2 years course after the Btech

If you want to proceed further in the technical domain M.Tech would be the best or M.Tech+PhD integrated and if you want to opt for management domain MBA would be the best.

every field of b.tech have vast scope in their own.so choose that field in which you have interest

Go for some certification course's.
They can help you I think so.
Better go for more reference and take further step in your career.
All the best

I think you can. Just check the detailed notification by IBPS