Bihar

Yes, if the colleges have made such a quota available.

Yes, some government jobs require only 12th pass candidates.

No, I think you have to go to Kotak as it has a better atmosphere for study.

You must have high percentage, it will be difficult for you to manage.

Doing engineering from Bihar won't effect your career but if you pursue engineering from bad college (I mean from less reputed private college of Bihar) then that will effect your career. So according to me you should pursue engineering from a good government college which offers good placement opportunities.

Refer the following colleges:
-Patna College
-St. Xavier's College
-Amity College of Commerce, Art and Science
-Magadh University
-Nalanda Open University
-Jai Prakash Vishwavidalya.

The questions asked in the entrance exam covers basic four parts i.e., language (English, Hindi or any other), general knowledge, current affairs, print and electronic media. The questions are asked around these four aspects. This is done to analyses the knowledge bank of a student, how much he/she is aware of the surroundings. And your proficiency in your language is tested.
So, read newspaper daily, watch news channels, read books etc. It will definitely help you to appear in entrance exam.