BCA

Visit for details: http://www.btechadmission.co.in/
No, there is no entrance examination conducted by Christ University for offering admission to BCA course. The candidates will be selected and offered admission through the below mentioned selection process :-
1. Skill Assessment
2. Personal interview
3. Assessment of past performance in Class 10, Class 11/12, during the Personal Interview
Visit for details: http://www.btechadmission.co.in/.

Yes, you face difficulty in placement if companies visited your college. And If you placed then you will not get a decent salary with BCA Degree. Also, Growth is limited. In my opinion, BCA graduates have to do an MCA course then In this case 12th marks become secondary. They SEE the Academics score/CGPA/percentage of your MCA course only. Because They SEE Your coding skill and Development skill at this stage.

No, I am sending you a link. Please read it. BCA stands for Bachelor in Computer Application
link-https://www.shiksha.com/bca-bachelor-of-computer-applications-chp.

I am sending you an authentic link from where you get a list of all good colleges for BCA in Bihar. Please check it out. link-https://www.shiksha.com/it-software/colleges/bca-colleges-Bihar?st[]=103&bc[]=33&ed[]=et_20&rf=filters&ct[]=171&uaf[]=city
But In my opinion, Any Colleges of Patna university will be the Best.

As much as I can understand your question, you are going to pursue 12th this year and apart from BCA, you want suggestions to pursue other courses.
Well I myself is a student of MAKAUT and pursuing BSC in Media Science.
There are plenty of courses to apply for, since your background is Biology, you can go for BSC in Physiotherapy, BAMS, BUMS, BHMS, travel and tourism course, media, fashion designing etc.
Plenty of field is open for you, I'd suggest go where you feel you can do it well.

Yes, you can get admission for BCA with 54% in 10+2. You should have any of these: (Maths/ Computer Sc./ Information Practice/ Computer Applications/ Multimedia & Web Technology/ Data Management Application/ Web Application) a optional subject in your 10+2 to be eligible for taking admission.

In my opinion, It's Better to do MCA course after BCA. As Any certification course is not going to help you a lot after BCA. So I suggest you prepare for the NIMCET exam along with Your BCA. By the NIMCET Entrance exam, you get into Top 10 NIT's college for the MCA course. I share you a link of the NIMCET exam From where you get all information about it. Link-www.nimcet.in.