Exam

Hi Ritik,
You are not supposed to submit original documents for any counseling and admission process. You have to carry only the original certificates and at least one set of attested photocopies of all the documents at the time of counseling. This is also notified by UGC.

No, you can get admission in IITs and NITs by this score in JEE Mains as you have to give competitive entrance exam including SAT, MCAT, LSAT, GMAT, GRE, IELTS and TOEFL which are required for abroad studies.

You have not mentioned where do you want to apply. You may please reframe your question and reraise it on the platform for an appropriate we expert to reply.

CAT Exam Test Date: First week of December 2017
Online Registration for CAT: Second week of August to Fourth week of September 2017
Results Declaration: Second week of January 2018
Admit Card Download Window: Second week of October 2017
This is the recent year dates and if you are seeing for next year,

Most institutes state minimum eligibility to be an undergraduate B.Tech degree in Chemical Engineering. - The Indian Institutes of Technology have the added eligibility criteria of a valid GATE score, which is only relaxed for those who have obtained their B.Tech from an IIT with a CGPA of more than

Just go through the link for complete detail about the college you can get by your link provided:
https://www.shiksha.com/b-tech/resources/comedk-college-predictor

You have qualified which is very good. This will bring a confidence in yourself so I think you should drop one year and try your best to crack JEE Advanced which is your target.
All the very best.

Sorry to say you can't get admission through JoSAA counseling but as you are an OBC, then you must score more than 100 in JEE Mains to get admission through JoSSA counceling.

Check the link provided for complete details about the college you can get in the counseling according to your rank, marks, category and branch specified:
https://www.shiksha.com/b-tech/resources/mhcet-college-predictor