B.A

Entrance test will be held to take admission in various program of Patna Women's College.
You need to first apply for entrance test and after having in merit list based on test you will be able to take admission in it.
All the best!

You could opt for BA in PS after completing class 12th with arts. A lot of opportunities are available students with BA in PS.
All the best.

As long as you have a graduation degree in your hand, you are certainly eligible to join the course. Distance education should not be an issue.

It is clearly mentioned in the guidelines of Delhi University that you can't opt for economics (Hons) if you haven't studied maths till 12th. You can't opt B.Com (Hons) too but you can go for B.Com programme.

I don't know all the colleges in India which provide law course after BA but this course is known as 3-years LLB which is done after graduation & criteria is graduation certificate. After applying, you have to sit for an entrance exam. Durgapur Institute of Legal Studies
Durgapur Law college.
I've an idea of these 2 colleges which provides 3-years LLB course & this is under Burdwan University.

Nowadays, many new courses are emerging up and each of them has their own values. But as far as I know, Java is the course which in spite being so old, it's value is very much high. Even Google's CEO after graduating from IIT in metallurgy engineering did Java and now he is the CEO. So, as far as I know, you can go with Java.