Bihar

Hello Chandan,
You may refer the links below for the list of colleges in Bihar and Mumbai for BCA:
1) https://www.shiksha.com/it-software/colleges/bca-colleges-bihar
2) https://www.shiksha.com/it-software/colleges/bca-colleges-mumbai-all

Hello Aditya,
Yes, the students from other states can also apply for TNEA counselling. For that, you need to meet the required eligibility conditions. You need to apply for counselling at www.annauniv.edu. I think the applications have been closed on May 31st and the counselling process is about to start.
For more details, refer:
https://www.shiksha.com/b-tech/exams/tnea

You can pursue B.Sc in chemistry or botany.

Hello dear,
It's less predictable that you'll get admission into any government medical college courses at this score. However, you can try in private BDS.
All the best.

Hello Dear,
Kindly let us know your NEET score so that we shall be able to tell you the expected colleges where you can join in.
All the best. Feel free to revert.

Hello Dear,
Its less predictable that you'll get admission into any government or private medical or dental college at this score.
All the best. Feel free to revert.

You must face slight problem in choosing right college for you.
If you want to do engineering then you are not eligible for JEE Mains, so further in different field same problem will appear for you.
So, minimum of 60 is required.
I hope, it will help.

FIITJEE Boring road campus is best for IIT preparation if you have low budget then try in Mentors Eduservs it is also a good coaching for IIT preparation.

Kolkata is the best.