IIT Preparation

Dropping a year for cracking JEE is a good option, provided you have will and dedication to remain focused on your objective. You require a plan to crack JEE. You may seek external support to overcome your weak areas. It is worth to try for it.

That totally depends on your grasping power and how you manage your daily schedule , make a daily plan and focus on your weak areas first , in 10-15 days you will get an exact idea on which subjects you need how much time and the overall time needed

You should firstly work on clearing your basics.

1. Master Mind
2. Chitra
3. Vidya Question bank

Both 11 and 12 class syllabus is important for IIT entrance exam, better focus on 11th syllabus during class 11 so that you will have less load in class 12.

go for council you'll get a government college

Yes there wont be any issue and you will treated as a normal student, gap year in between graduation creates problem but before taking admission it wont create any issue

next year Your boards marks r not going to be considered so better u concentrate on Your JEE preparation

Hi Sahil,
List of colleges offering JEE coaching classes, kindly refer the link below:
http://goo.gl/XF65wB
Kindly filter out the branch / college / location as desired from the above link.
I hope this information helps. Please feel free to revert.
Wish you luck.

Ofcrouse CBSE is best among those,no doubt.best of luck!!