GATE

GATE exam is required to do M.Tech and also to get into some PSU (government-owned corporations are known as Public Sector Undertakings (PSUs) in India).

There is no college by the name, GATE.

Yes, it totally depends on you if you want to prepare or not. There are several extra opportunities inside and outside VIT for GATE preparation. You will get a platform to improve yourself and prepare for GATE level.

You can apply for M.Tech in private college and someone low-grade government colleges.

Well, the course offered by IISC is more research -centric which leads to a different field and not as much favourable in getting the highest paid job. While, NITIE offers the courses which are more aligned to Technology and industry and the one who wants to pursue MBA from here so yes it is the right place to look for.

Hello Kamal,
You may refer the link below to know the eligibility and admission process for M.Tech in food machinery and power at IIT KGP :
https://www.shiksha.com/engineering/course/m-tech-in-farm-machinery-and-power-indian-institute-of-technology-kharagpur-293507

Yes, if anyone get a seat through counseling after GATE exam in any college he/she will get a stipend. So whether it is IIT or NIT you will get stipend.
All the best.