IGNOU - Indira Gandhi National Open University

The eligibility criteria for IGNOU BLISc course is any of the qualifications:
*Bachelor's degree with 50% marks ( 45% for students of SC/ST/OBC/PH category)
*Bachelor's degree with a Diploma ( one year) in Library Science
*Bachelor's degree with two years of working experience in a Library & Information Centre.

Yes, you can definitely give the exam and clear it. This way you will be eligible to do B.Ed.

But you have to prepare yourself first for the entrance exam or get your name in the merit list as per your percentage.

Hi, You may take a break or exam leave during your exams, or you may pursue your course via correspondence.

Both are UGC certified universities. However, Calicut University is offering regular course whereas IGNOU is only providing distance education. Most of the private companies don't accept IGNOU certificates, moreover they consider it as a second class. Therefore, there are some troubles with IGNOU certificates. Luckily, there is no issue with government sector jobs. Both certificates are valid hence it is UGC certified. However, you may have to face some troubles with IGNOU certificates. Therefore, if you have enough time to do a regular course, go for Calicut University. If you don't, then go for IGNOU.

Indira Gandhi National Open University, known as IGNOU, is a Central University located at Maidan Garhi, New Delhi, India. However, if we look in to the support structure IGNOU provides for its students then yes, IGNOU is a good university. The whole working body works as one including the regional center and the study center.

I think, you have to go to the IGNOU regional office which is located in Rajghat, Delhi.

All these MBA programs are available in IGNOU University ; https://www.shiksha.com/university/ignou-indira-gandhi-national-open-university-Delhi-3030/courses/mba-pgdm-bc
Follow the link and get to know what options you have in Masters from IGNOU.