B.Tech

Please visit this college predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

SAEEE is the entrance exam for the Sathyabama Institute of Science and Technology for the course B.Tech in biomedical engineering.
For further information:
https://www.shiksha.com/b-tech/course/b-tech-in-biomedical-engineering-sathyabama-institute-of-science-and-technology-jeppiaar-nagar-chennai-33273

Frankly speaking, IIITs are well known for information technology courses. It's quite tough to differentiate between these institutions. However, to help you I am attaching a link that will give you all the required information about not only these institutions but all the colleges in India which are offering this branch for studies.
https://www.shiksha.com/b-tech/ranking/top-computer-science-engineering-colleges-in-india/46-2-0-0-0
Best wishes to you.

The commencement of filling of form for B.Tech programme began on 10 May 2019. Please visit this page for important dates:
https://bitmesra.ac.in/UploadedDocuments/admadmission/files/BTech DJP 2019 - Important Dates. Pdf

Yes, it is good for B.Tech from mechanical in PSIT as it has good placement records for all branches.

I have heard that TMU is a good university and also has good placement records. I can say that you can pursue it. Also, you can use Shiksha college comparing tool and NIRF ranking.

You have to appear for PSC (Public service commission) to get into the services for government job of the state where you want to do the job. Regarding jobs in private sector, you have to visit the company's website for vacancy.

It depend upon you what you want to choose both courses are good where your interest lies but according to me B.Tech in food technology is better scope you have a good no of vacancy in government dept for same.
Sorry but according to last year cutoff your selection chances are very less.