B.Tech

https://www.shiksha.com/mba/colleges/mba-in-supply-chain-colleges-india
Go through this link and choose a college according to your score and knowledge.

Yes, EEE students are perfectly eligible to give IES. They can select either Electrical or Electronics to appear for Examination.

https://www.google.com/amp/s/www.shiksha.com/engineering/articles/amp/what-after-btech-know-your-options-blogId-14784
This will guide you proper what to do after B.Tech.

Hi,It is somewhere based on your interest. If you like technical things you may go for B.Tech, as it comprises more of technical things and if you like playing with the numbers, you may go for B.Sc. Stats and it even have good career options ahead. You may also predict your college and then decide. I am sharing a link for the prediction. Other than there, various aspect you can decide on like fee for B.Tech is more and it's a 4 year course while B.S is a three year course.
All the best
https://www.shiksha.com/b-tech/resources/mhcet-college-predictor.

You may check this link:
https://www.shiksha.com/articles/engineering-entrance-exams-in-india-blogId-5645

There may be problem in placement as all big companies placement cutoff is 60% and above throughout the carrier. So ,You have to face such problem when you seat in placement. But VIT is so good college you will get place in companies who criteria is 55% and above .Or you may develop skills and do more and more internships to build your resume awesome and effective and score good marks in semesters that will definitely help you or you may go for gate exam or higher study .