Engineering Entrance Exam

You should refer the following books for the same:
Chemistry-NCERT (class 11th and 12th)
Maths-Objective Maths by R.D. Sharma
Physics- H.C. Verma

There can be two choices -
If you have scored a good percentage in 12th board exams then you can prepare for JEE Mains by yourself. For this, you can also refer to the study material of ALLEN, RESONANCE or VIBRANT coaching institute. In this case, you can complete your first year of polytechnic also.
The second one is, if you have not secured good percentage in 12th boards then refer to a good coaching institute and try to score good marks in JEE Mains.

Sorry, you can't do it as it requires 10+2 but you can apply for lateral entry in best college like MIT or government college without doing JEE Mains in B.Tech. it's an easier way but you can not appear for IIT.

Yes, its good to take a chance. If you clear your JEE exam then there will be no problem to get the admission. If you couldn't qualify then you will have another option without any loss.

It is IAS because it has more syllabus.

You must be in top 400-500 rank holders in IIT JEE advance in order to get admission in IITs.

Eligibility for GATE examination is a B.Tech/BE/AMIE or M.Sc. After 12th you can appear for JEE.

Eligibility is a Bachelors degree in Engineering/Technology (4 years after 10+2 or 3 years after B.Sc./Diploma in Engineering/ Technology) and those who are in the final year of such programs.

In boards exam 60%+ is better. For CSE in Jadavpur, this year cut off was about 286 rank. In short, you need to get 120-150 out of 200 marks in WBJEE.