BCA

Best BCA government colleges in Kolkata are:
1.Annex College of Management Studies
2.Institute of Engineering & Management
3. B.P.Poddar Institute of Management and Technology
4.Annex College of Management Studies
5.George College of Management & Science
To know the exact scenario for faculty and placements for each college, get in touch with the current students through social media or in person.

Not possible, if you clear all the backlogs then you can try to pursue BCA.

Regarding the subject in UGC NET entrance exam, I am afraid its not going to be your choice. You can appear only for the Computer Science and Application and that is the end of the story. The subject is selected based on the post graduation qualification. Not the graduation course that you have taken.
Therefore you can not select between Maths and Computer Science. Your post graduation degree is Master of Computer Applications therefore the subject will be Computer Science and Applications.
Regards.

You can opt for BCA, but its hard to study if you don't know the basic computer knowledge.

Dear,
BCA is a three years' Bachelor degree course that can be pursued after completion of +2. After the successful completion of BCA you will be treated and certified as a graduate from a UGC recognised university.

The basic eligibility criterion to pursue BCA course is class 12th. You should score an aggregate of 50% in the class 12th. You should have taken mathematics as the main subject at class 12th level. There are many reputed colleges in the country which offer BCA courses. Some of the colleges are Garden City College, Bangalore, MS Ramaiah Junior & Degree College, Bangalore, Amity School of Computer Science, Noida, Apeejay Institute of Management & Information Technology, New Delhi, etc.