B.A

This course is done as a full-time course at Jagran College of Arts, Science and Commerce.

Yes, admissions are open you can apply.

In IGNOU, B.A. Is a direct admission course. Admission open for July-2018 Session. Last date for fresh admissions in Certificates and Diplomas is 30th June, 2018
Last date for fresh admissions in Bachelors and Masters is 15th July, 2018.

It provides BA in economics (general) and not honours.

No, you can't, but you can pursue post-graduate Diploma courses.

Yes, you can pursue Diploma courses and you should choose branches as per your interest. After Diploma, you'll get good job options in both sector private and government too.

These following colleges offer this course:
1) Mata Sundri College for Women, University of Delhi
2) University of Delhi
3) Indraprastha College for Women (University of Delhi)
4) Shaheed Sukhdev College of Business Studies
5) Delhi College of Arts & Commerce
6) Jesus and Mary College
7) Kamala Nehru College
8) Janki Devi Memorial College
For more information visit the particular college's website and DU's official website.

No, application form started from December 8, 2017, so I don't think that application form are still available.
You may go for another university. There are many option available. You can try in those university.
All the best.