B.A Political Science

Yes, St. Xavier's College, Kolkata does offer B.A. (Hons. ). In Political Science. For further details regarding this course, please refer to the link provided below:
https://www.shiksha.com/humanities-social-sciences/political-science/course/b-a-hons-in-political-science-st-xavier-s-college-Kolkata-park-street-83765.

Delhi University, colleges under Calcutta University, etc. are the best for B.A. Political Science Hons.
Other colleges are also there-
Please check this link once.
https://www.shiksha.com/humanities-social-sciences/political-science/colleges/b-a-colleges-india

Yes, DU offers Army quota.

Yes, with 82% marks in boards, you are eligible for admission.

Yes. If it is possible for you to drop, then you can because it is better to pursue a course in which you are interested rather than doing some other course.

Hi Sake, Hindu, Hansraj and Ramjas, in the order of naming. They all are a part of the amazing North Campus. This brings you not only excellent campus life, but also some superb cafeterias. I didn't have a pretty nice experience with people at Hindu, but in spite of that, my vote goes to it. All the best.

The minimum aggregate required depends solely on the cut-offs which are released. You need to score around 96% at least to get admission in LSR. Last year, the minimum was 97%.

You can get any publication books for JMI B.A. (Political Science) from online or from Jamia Maktaba. The book will guide you throughout your preparation.

Hansraj college, Delhi University
Hindu college, Delhi University
Delhi college of arts and commerce, Delhi University
Sri venkateswara college, Delhi University
DAV college, Chandigarh
GGDSD college, Chandigarh
Kirorimal college, Delhi University
St. Xavier's college, Mumbai
These are few of the best colleges in North India for political Science honors where you can apply.
Good luck!