B.A

Getting admission in a regular college is no possibility. Distance education is the only way you get an undergraduate degree. Then you may enroll for a regular Masters degree program after successfully getting the undergraduate degree.

CAT exam coaching duration is 6 to 7months based on the institute. Ideal time for joining coaching is final year (i.e. June to November), so that you can write exam in December. TIME institute is good.

It can be possible, however you can only do it through open, if you have the SY BA proof.

Yes, you can as the marks doesn't matter.

You are eligible to do MA psychology from Delhi University, if you have scored more than 60% in graduation degree. You will have to appear for MA psychology entrance examination conducted by DU.
You can refer to following link for further details:
http://uic.du.ac.in/images/Department of Psychology (Faculty of Arts).pdf

You can do LLB after completing B.Com. Why you want to waste your 1 year?

To get admissions in law course, you minimum need 60% marks in your boards and a good score in CLAT. Other than PU, you should also apply to these colleges for more options and opportunities:
University, Bangalore (www.nls.ac.in)
WB National University of Juridical Sciences, Kolkata (www.nujs.edu)
NALSAR University of Law, Hyderabad (www.nalsarlawuniv.org)
National Law University, Jodhpur, (www.nlujodhpur.ac.in)
Campus law centre, Delhi (http://clc.du.ac.in/)
UPES, Dehradun (www.upes.ac.in)

Below mentioned are the best courses after BA in India:
1. MA.
2. MBA.
3. B.Ed.
4. LLB.
5. PGDM.
6. PG Diploma.
7. Hotel Management.
8. Certificate courses in journalism.
9. Mass media.
10. Event management.
11. Travel and Tourism.
12. Fashion and interior designing.
13. Animation and
14. Film studies.

To become an IAS officer, one needs to earn a Bachelor Degree and prepare smartly and extensively. BA Hons in subject of social sciences will do well.