Swami Vivekanand University

B.Ed is of 2 years duration course and it is a regular course.
For more information, click here:
https://www.shiksha.com/university/svc-swami-vivekanand-university-sagar-42926/courses/bed-bc
Hope it helps you.

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The applications will begin tentatively in the month of June. Exact date has not been announced yet.

Yes, you can go for B.Ed through IGNOU.

Interested candidates can apply online with required information. The admission is based on the marks obtained in 10+2 Examination. Website: http://www.svnuniversity.co.in

Swami Vivekananda does not offer BA course. I don't think so that they have a center in Kolkata.
I would suggest you to contact the college to verify the same.
Here is the link: https://www.svnuniversity.co.in/mainsite/contacts.aspx