Bihar

Hello there! I am sorry my friend, but the minimum marks required for this course are 75% in 12th with PCM and a respective JEE Main score, so with a heavy heart, I have to tell you that you are not eligible, but you can try in other colleges where the eligibility criteria is less or lower percentage is required or you can also try in some private university or college.
Good luck for your future.

Hello,
Kindly go through the below mentioned link:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

You can get admission in BIT Patna.

Yes, you are eligible for that.
To have an admission in GLA University for Diploma in computer engineering you need to pass 10th examination with atleast 40% marks and mathematics as a compulsory subject.http://gla.ac.in/course/33

Yes, you can get admission into Patna Women's College for BCA with 59%. You're eligible for admission into this college.

Yes, you can get your name changed. Just contact the education board you completed your SSC from.

There are various coaching institutes in Bihar for preparation such as Vidhya Mandir, Super 30, Vision Classes and Resonance.