Colleges in Kharagpur

Yes, they provide good placements facilities to executive MBA aspirants.
Visit the link for details: https://www.shiksha.com/business-management-studies/course/executive-mba-vinod-gupta-school-of-management-indian-institute-of-technology-kharagpur-168740.

You need to qualify JEE Advanced and after that, you need to appear for AAT (Architecture Aptitude Test, for IITs). If you qualify that, you can proceed for B.Arch in IITs.

Hello Nirnjan,
I am attaching a link that will give you all the required information.
https://en.m.wikipedia.org/wiki/Joint_Admission_Test_for_M.Sc.

Aerospace will provide you with more opportunities abroad but ECE will give you loads of opportunities in India itself. Though the thing to consider here is that, IIT Kharagpur is an old IIT & much more established than any of the new IITs which will very much be visible during placements and in other avenues. Please decide accordingly.

It is just fake news that you have got and nothing else. Both the institutes are participating in JoSAA 2018, as usual.