B.Tech Counselling

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Go to the college predictor link I am sharing here. You can predict your college according to your rank.
Good luck.

According to rule, if the family income less than 200000 and with very high rank, one can easily pursue and take benefit of tuition fee waiver scheme. You can easily check date of counseling online in university website.

No, it is not necessary to qualify JEE Mains to take admission because many colleges provide admission directly and many through there own entrance examination, if the college you are interested in accepts only JEE Mains result than only it is necessary otherwise if they provide admission directly then you don't have to clear any entrance exam and in case of there own entrance you have to clear that.

No, the counselling fee is not refundable.

You need following originals at the time of counselling:
Your counseling letter
UPTU score card
Your original marksheetsMedical certificates
Caste certificate
Domicile certificate
Income certificate