Calicut

Kindly predict your college through this college predictor. The rank predicted might not be accurate, but it certainly gives an idea to the aspirant.
https://www.shiksha.com/college-predictor

Sure, you can take admission in MBA in good college by applying state PGCET CMAT and other MBA entrance exam. You can go ahead all the best.

For this query, you have to directly contact the college administration.

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.

The last year closing rank at NIT-Allahabad and Calicut in your category were 2381 and 2227. Hence, your chances are average here.

You can follow the link predictor for better results:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

NIT, Trichy is better than SPA, and even highly difficult to get admission in, you must have more than 99.6% in order to get admission in NIT.