Engineering Entrance Exam

Of course, you can if you wish to. Nothing could stop you there. The ECE branch is good and faculty and infrastructure is great. The only problem sometimes is the placement in core ECE companies. But potential candidates in the branch have always performed well despite that and gotten placed in very good companies.

Yes,
You should go for counseling.
You will get admission in newly admission IITs for sure.
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx
Check this branch and IIT college predictor.

Yes, you will definitely get into IIT.
Your available choices are:
IIT, Dhanbad
And other newly opened IITs in past 3 years
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx
Check this branch and IIT college predictor

Hello Akash,
IIT-JEE preparation is, to some extent, irrelevant of the classes you attend. It requires immense practice and clarity in all the concepts that are asked in the exam. All the classes that provide IIT-JEE coaching are good, at the end it depends on your efforts.Again, remember that it is not difficult to crack IIT JEE exam. All the best for preparation!

Sorry, but your rank is too high.
At this stage, there is no IIT available for you.
However, you may get predatory course in IITs.
Best of luck for future.
Any queries are welcomed.

Sorry to say, but you haven't cleared JEE Advanced required cutoff.
So, there are no chance of getting admission in any of the IIT.
I hope you understand my point.

Yes, you will definitely get admission in an IIT.
You scored very good marks in JEE Advanced.
No need to worry about it.
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx
Check this branch and IIT college predictor.

Sorry to say, but 96 marks would not help you to fetch any of the IIT.
However, you can enroll for preparatory courses offered by IIT at this stage.
Best of luck.

There is a link below that will help you find a college that you might get into with your score/rank:
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx

Yes, you can try for NIT's. Your category quota might fetch you a seat in one of the NIT's. NIT Hamirpur most probably because previous year's closing rank was highest for NIT Hamirpur.