Colleges in Warangal

Yes, it is good for MBA in terms of placements.

NIT, Warangal doesn't accept ICET score. You should appear for MAT, CAT, CMAT or XAT exam to get admission in the same.

Dear Khaja,
Try at Kakatiya University. If you really want to do MBA then try for B-schools at Hyderabad.
All the best.

NITK is the best.

You can check through links mentioned below :
https://www.resonance.ac.in/jee-main-answer-key-solutions/jee-main-2016-rank-predictor.php
https://www.shiksha.com/jee-mains-college-predictor

CSE NITT is the better option

Depends on the branches you are getting in each of them and which branch you want.To get better guidance you can specify your rank and other details so I can guide you accordingly but in general I can say this that all are good options but among them for CSE/IT branch ISM Dhanbad and IIITA will be better options considering the placement and the reputation.

It depends on your institute. Some institutes don't have internal sliding. Some do have it and Its either at the beginning of first year or the end of it. A notice will be given to you by your college. You will have to fill up a form and depending on the vacancy and your grades you might or might not get a change of branch.