Bihar

See, if you clear those exams then you can easily appear for the paper but before that appearing for the paper is of no use.

Kindly name the college correctly as I am not able to fetch any college name with the one that you have provided.

Yes, you appear for IIT IN 2017.

Except Jadavpur University, each and every government engineering college considers a West Bengal domicile as a must.
Even though you have a Bihar domicile certificate, you can get a WB domicile, but in some cases. Visit the WBJEE site, you'll find some formats. Those are for domicile certificate required to be shown in Reporting Centres after counselling. You can get the certificate only if you are residing in West Bengal for more than 10 years or if your parent (s) are resident of Bengal.

I do not have any concrete information about Mahatma Gandhi University, Kolkata branch in Bihar or Patna. But, Mahatma Gandhi Central University is available in Bihar.
Please click the link below for more information about the university.
http://www.mgcub.ac.in/.

Yes, it is good. But the suggestion is to visit personally for getting the knowledge on the facilities and infrastructure.

Hi, Please find the related link below:
https://www.shiksha.com/it-software/ranking/top-bca-colleges-in-india/96-2-0-0-0
https://www.shiksha.com/it-software/colleges/bca-colleges-Patna.

Rank 1 : Vidyamandir Classes Patna
Rank 2 : FIITJEE Patna
Rank 3 : Mentors Patna
Rank 4 : K Singh Vision Classes Patna
These are some suggestion. God bless you and have a nice day.

HS Civil Engineering 20991 33304
HS Computer Science and Engineering 4732 11618
HS Electrical and Electronics Engineering 14924 24345
HS Electronics and Communication Engineering 13443 20955
HS Information Technology 12001 14868
HS Mechanical Engineering 21308 28495.