Colleges in Kerala

https://www.shiksha.com/college/sim-saintgits-institute-of-management-kottayam-30931/admission
This link might help you.

Your TANCET % of marks is very good enough for MBA admission. Hence you will get the admission here.

Yes, you are eligible. The eligibility criteria is 10+2 with minimum 60% of marks and entrance test. You will have to go through the prospectus of the course provided by the college to know more.

The path which you are looking for is really appreciated. Regarding space and research Science courses and their fee structures, you can go through below link
https://www.shiksha.com/university/iist-indian-institute-of-space-science-and-technology-Thiruvananthapuram-25141
All the very best.

The admission in both (IIST& IIT) are based on ranks obtained in JEE Advanced (Conducted among the JEE Main qualifiers). Candidates who are desirous to join the Undergraduate and Dual Degree Programmes offered by IIST are required to apply separately to IIST through the online application portal (http://admission.iist.ac.in) and complete the registration and fee payment process. Further both IIST and IIT-B are premier institution of National importance, Hence no comparison can be made.

https://www.imi.edu/delhi/placement
Kindly visit the given link to know in detail all about the placement stats of the full-time PGDM program of IMI, New Delhi.