BCA

BCA saves one year, as syllabus of BCA is more or less same as B.Tech. The only difference is in the 1st year, where B.Tech include engineering sciences- mathematics, physics, chemistry etc. BCA syllabus does not include electronic paper I, II & III during 2nd, 3rd & 4th Year. Bottom Line: The companies who recruit B.Tech candidates are the same that recruits BCA candidates.

Normally, people studying from IGNOU are working executives and cannot devote all their time to studying a particular course. If that is the case with you, please go ahead and take up BCA from IGNOU. However, if you are not working anywhere, and can attend regular classes you should apply for a regular BCA from a reputed institute. Regards.

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.