M.Tech

Both, M.Sc. and ME have research based and course based program. ME will contain more hardware papers whereas M.Sc. will concentrate more on SW. After M.Sc., you can go for PhD. Length of both the courses is 2 yrs.

Indian Institute of Science, Bangalore, India
IIT Gandhinagar
IIT Guwahati
IIT Kanpur
IIT Hyderabad
These are some institutes in India which provide M.Tech in Signal Processing domain.

Why not? If you meet the requirements you can. See that you have good academic grades and take the IELTS or TOEFL. You must contact the college for admissions in MS as your visa will be valid only for four years initially. You can also look for integrated options or pathway programs.

According to me MBA has much more and better job prospects as compared to M.Tech. After pursuing MBA, you can apply for government jobs as well.

It is up to you. If you want to study, then opt for B.Tech and M.Tech, otherwise, get a job. If you increase your study level, you will get more knowledge of your subject, and you will get better job prospects too.

You will be able to get a teaching job in an engineering college based on your M.Tech, but you need to pursue Ph.D for your career growth.

No, if you have backs then how will you produce your mark sheet in M.Tech.