B.A

Check out with some of the colleges under IP University who might be having spot admission facility. I mean they might be offering admission without counselling or entrance. This you need to check. A more valid option shall be Amity School of Communication which is more likely to grow into a good place for mass media and media related education.

There is no procedure to complete BA in one year.
You have to go through the whole process.

https://www.shiksha.com/arts-fine-visual-performing/music/colleges/b-a-colleges-india
Go through this list.

Not possible at all. You can choose to obtain fake certificate from a local shady college but that is not recommended. It is a 3 year course and will require 3 year attendance.

The admissions started in month of May. I don't think so that they are granting admission now. Once you can get in touch with the college authorities to know the same.

In the NET exam, you need to select the same subjects in which you have done your post-graduation. You can't choose Urdu after doing M.A. In economics.

Yes, you can. Contact local IGNOU center for details on admission and fee. It is legal and accepted widely.

BA is like a vast field and BA in mass media which we also know by the name of B.A. in journalism is a sub-branch of Bachelor of arts. You can easily opt for your chosen stream in B.A. There are many courses available in BA. They are
BA in psychology, BA in political Science, BA in agro services, B.A. in public relations, B.A. in cinematography, etc.

Talk to school administration or register for correct course.

Yes, you are. You can fill all type of exam forms. IGNOU is UGC approved and accepted by every exam conducting authority.