B.A

Dear Narinder,
You must pass all the subjects.
Eligibility- 10+2 or its equivalent examination with at least 50% marks (45% in case of candidates belonging to SC/ST category) in any stream conducted by a recognized board/university/council in aggregate.

Yes, you can take admission in Fergusson College.

Yes, you can do BA in psychology from various colleges such as:
1. Lady Sri Ram College for Women
2. Zakir Husain College
3. Daulat Ram College
4. Bhim Rao Ambedkar College
5. Gargi College
6. Kamla Nehru College.

Yes, you are eligible for doing B.A. B.Ed even after completing your Intermediate with Science or from any Science stream. There will not be any issues. You can do your desired course.
Best of luck.

Hello Amana,
You are in a typical Shakespearean dilemma! But do not worry. Both these colleges have good reviews and I feel you can take admission in any one. Preferably you should choose one where your friends are also seeking admission. Another criterion could be ease of commuting.
Best wishes.

If you don't live in Bihar, then I think yes. I am providing you the following link so that you can check the locations of the study centres:
http://www.nalandaopenuniversity.com/admission.html

66% is too less for BA in Xavier's. It's really not possible to get in with that score. Still if you fall in Christian minority then you may try.

If you are from general category, then it is very low chance to get admit in this course, because the cut off of this course closed in above 90%. But, you had a little chance in out of campuses colleges.
If you belong to OBC category, then you must get admission for this course. Mostly in last 3-4 cut off, you will get admit for this course.
For more information regarding admission process, visit DU website.