M.Tech

Yes, you still have a chance in getting a seat in IDP (B.Tech +M.Tech ) in Mechanical Engineering or Civil Engineering .Also, don't forget to check with EEE (IDP) also. This year, there may be a chance.

Hello dear,
Admission in universities or institutes offering B.Sc in Agriculture course is done basically in two modes. It is done either based on the marks obtained in the qualifying examination (Direct Admission) or written exam conducted by the university/institution that offers the degree.
The details on how to apply for B.Sc degree in Agriculture can be collected from the authorized website of the institution along with the information on course details and available number of seats. The application forms can be obtained either through the college office or from the concerned web portal.
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No. You can't get admission for M.Tech. You need to pursue BE or B.Tech degree first.

Yes, there are chances. I mean, you can get admission in VIT but for that, you have to qualify their entrance examination. Without qualifying exam, you cannot get admission. I hope this helps.

Yes, you can apply for it. For other information, visit this official link
http://admissionas.jdvu.ac.in/jadavpurBed/index.php

MIT offers 2 years M.Tech in Bio-Engineering research. It also offers integrated course in bio engineering, check the below link for more details-
https://www.google.co.in/amp/s/www.shiksha.com/b-tech/course/amp/integrated-b-tech-m-tech-in-bioengineering-mit-school-of-bioengineering-sciences-and-research-mit-art-design-and-technology-university-Loni-kalbhor-Pune-257654
If question is about bio medical engineering, then Ajinkya D. Y. Patil Institute and College of Engineering Pune are the options.