Science

Hey Ujjwala,
You surely can. I am attaching below a link to sort all your queries out:
http://distance.bharatividyapeeth.edu/index.php/courses/arts-commerce-and-social-science
Feel free to raise more queries.
All the best.

You cannot do your Bachelor's twice. But, you can apply for Masters in journalism and mass communication. It is the option you should go for (MJMC).

For a career in counseling, after 10+2 one can do their graduation in subjects like psychology, social work etc. And can go for post graduation in counseling, Life skill education or psychology from an accredited educational institution. Candidates who have Masters degree in any area are eligible to

Yes, it is compulsory to have Maths in +2 and pass in it. Clads 10 CGPA doesn't matter because admission is on cut-off basis of 12 Boards percentage.

B.Sc in physics chemistry and CS are good options for future. Christ is a good option, MSR, Presidency, Surana.

Lots of Government as well as Private job opportunities are present in front of Graduates. Talking about Government jobs, State Agriculture Departments recruits Graduates to fill up Officer level posts. Government Banks also recruits Graduates to fill up Officer level posts.

Yes, you can pursue but you need to work harder. Psychology is a vast subject which requires lot of practical knowledge. You should also read graduation level psychology as it will be helpful in your M.A.

Yes, they are eligible to attempt the entrance exam. You need to prepare well for entrance because there is a lot of advanced syllabus than what it is in CBZ. One of my friends has cleared the exam. Hope it helps.