Engineering Entrance Exam

Yes, you are eligible.

You should appear for JEE mains first, if you clear that exam then you should appear JEE advance.

Yes, every candidate who appeared for JEE main and has been allotted AIR is eligible for JOSAA counselling, but the seats are allotted on the basis of merit. You can fill in your choices for the spot round.
Best of luck.

It depends upon overall percentile. 180 - 200 score may give you under 2000 (OBC) rank.

No, you can write GATE examination either in your final year or once you've completed your graduation degree. It is usually held in the month of February once in year. So, you can give GATE exam in February 2018 or later. Not in 2017. For cutoffs and colleges, look up in counselling and MBA heading of https://shiksha.com.

You just need to be in the top 20% in order to go for JEE. And the percentage scored in class 12 will be considered only. Instead, from next year onwards, class 12 marks will no longer be considered in the JEE.

GATEFORUM, TIME and Career Launcher are the best coaching centres in Ahmedabad for GATE.

I would recommend, GK Publishers or The Pearson Guide to GATE.

No, it's only for JEE advance.

1. For physical chemistry: PW Atkins.
2. For inorganic chemistry: JD Lee.
3. For organic chemistry: Morrison and Boyd.
4. For physics: HC Verma
5. For mathematics: Arihant Prakashan.
Also, you can buy DLPD books of Kota's best IIT classes (like Resonance, Bansal and many more)
If you get DLPD, you will get better rank than reference books. And, don't forget to refer NCERT books also.