CBSE 12th

You need to appear CAT and score above 95 percentile.

If you are facing a genuine problem, then you can probably drop a year. Other option is also available for it. You can request for a helping hand like if you are unable to write exam yourself, on behalf, a third person can write exam. You have to dictate answers to him and he will write. Also, you may also be provided some extra time. For these options, you have to take permission from school authorities and respective board authorities like CBSE.

You have good chances of getting a call for GD & PI.

Hi,
Other than IITs and NITs, you can take admission in some CFTI which you can get by the same JEE exams such as IIEST.
But if you want other than JEE colleges, I would advise you to go through state engineering colleges or some private colleges.
Jadavpur by WBJEE, BITS PILANI, VITEEE, etc.
I hope it will help you.

Hey, It totally depends on the selection criteria for the admissions in that particular year. Just focus on the preparation for the GDPI WAT round and you might actually make it through. If it helps, the 2017 admissions selections criteria was: CAT Score-55%, GDPI WAT-30% and others (10th, 12th, Academic diversity, Gender diversity, Work ex)-15%. Please note that the criteria may change. All the best.