Certificate

This answer can be given by the institute itself. Just visit the college website if provided on internet or visit the college and try to get information there.

Yes. Students of a category compete among themselves. They are selected on the basis of their category rank.

The certificate course of food and nutrition is available at the BR Ambedkar Open University, Hyderabad. It is a 6 months part-time program.

No 3-month courses can give you complete knowledge on statistics and analytics anywhere in the world.
Its a huge subject and requires at least a year or two to get some knowledge (Way more for complete knowledge). Whereas, about the six sigma black belt training, ISI offers that but is of 6 months duration as of my knowledge.

Hi, Please find the link below:
https://www.shiksha.com/teaching-education/exams/ctet.

Yes, surely, this helps but it depends upon the official authorities.

Migration Certificate will be provided by the College you studied in. Ask them for it and they will give it to you. And yes, you can take admission in CCSU if you have proper Bachelor degree with 50% marks.