I know I can't get CS in NIT suratkal still should I put it in my choice in JoSAA counseling.

Candidates can check the JoSAA cutoff on the official website - josaa.nic.in.

Yes, the JEE Main admit card is needed at the time of JoSAA counselling.

Yes. You can. Both counselling have different purposes. JoSAA is for admission to IIT and NIT+ system, while JAC Chandigarh is for admission to  Dr S. Bhatnagar University Institute of Chemical Engineering and Technology; Panjab University, Chandigarh (Formerly Department of Chemical Engineerin

• Candidates should have JEE Advanced rank.
• Candidates must have at least 75% aggregate marks in class 12 and SC, ST and PWD candidates must have atleast 65% marks.
• Candidates must be within the category wise top 25 percentile of successful candidates of their respective class 12 boards.

No, your candidature will be rejected as you need to have minimum of 75% in class 12 to be eligible for admisison to the IITs, NIT, IIITs and GFTIs via the JoSAA counselling. Even if you pass JEE Advanced and JEE Main, of you do not have 75% minimum marks in class 12 boards you will no get admission