B.Sc

Prabhakar,
You can go for both and after LLB, you can appear for tests meant for selection of judges. But, it would be better to go for Integrated LLB, where you will be saving one precious year of your life along with fee for one year. Also, you will get a chance to earn a year before.
There are many good universities like LPU, Sharda, Sastra, etc. that are offering 5 years integrated LLB. All these universities have wonderful infrastructure and world-class facilities to offer to students apart from good placements that they offer. Some even offer scholarships.
Good luck.

Yes, you can pursue B.Ed after completing B.Sc. Graduates in any stream may look to pursue Bachelor of Education [B.Ed] from a recognized institution. Admission is based on either through entrance examination or marks obtained in the qualifying examination, whatever may be the admission criteria of the institution applying for.

B.Tech is better than B.Sc in terms of everything.

Dear,
Psychology one of interesting and challenging field in today scenario. If you check the record of Depression cases that will be above 5 crore cross.This field require passionate and dedicated psychologist .Don't doubt about this programme ,You would get good opportunities and income too
All the best.

Dear,
Specially in research field like Biotechnology, Microbiology, stem cell and life science you would get good opportunities after Masters and PhD level. You won't get much opportunities after B.Sc or B.Tech degree. Specially in India this field don't have good salary structure .Either you need to get few years of experience abroad then settle in India.

Hi,
Kindly refer to this link:
https://www.shiksha.com/science/colleges/b-sc-mathematics-colleges-india

I think you mean IIM Trichy. The answer is no. The cut-off for being shorlisted for call is 96.7 percentile for general category