M.Tech

B.Tech there is Jee mains entrance exam for master degree there is no such requirement.
You can take admission in VIT Vellore on Merit Basis.
Best Of Luck,

You have to go for Gate examination as it is basic criteria for doing M.Tech in engineering college. This criteria is applicable for SVNIT also. So, all the best for future.

Yes,
As you know that KNIT is a part of AICTE approved Institute. That's why it provide stipends.

I'll refer you to join B.Tech CSE rather than integrated 5 year course because if you change your mind in 4th year of your graduation seeing that time scenario then it will be better for you to join MBA or by qualifying GATE you can join any of the PSU because joining integrated course is only beneficial if you have clear goal to join in research or be a professor in any college.

Yes, with 293 AIR in GATE aerospace engineering (2017), you will definitely get admission in mechanical engineering for M.Tech. Your rank is too good and on the basis of that, you will get admission.
Best of luck for your future.

No, because the things you learn during the research time under the guidance of professors can't be learned from distance education.

You have options from being a teacher and even do research work in your field.

The chances are high if you do M.Tech from a renowned university.