JEE

To study organic chemistry, you can opt for SK Malhotra and to learn mathematics, you can opt for the RS Agarwal.

Yes, you should appear for JEE but college stamp is required to fill the form for JEE.

You can collect all the previous year's questions. You should clear your concepts as well as rigid. You should practice as much as you can. Knowing the theory and formulae, won't help you.
Best of luck.

You need to keep your basic concepts clear. You should study from NCERT books for strengthening the basic concepts. Try as much application based problems as possible. You need to sit for 3 hours and in order to solve these problems. Try and solve all the previous years question papers.

You can refer to the following textbooks:
1. Cengage for mathematics.
2. Dr. OP Tandon for chemistry.

1. Physics: DC Pandey, HC Verma and IE Irodov.
2. Chemistry: OP Tandon.
3. Mathematics: ML Khanna.
NCERT must be referred, while preparing for IIT-JEE.

All parts are important, there is nothing like important questions, all the topics are interrelated to each other.

NCERT, HC Verma and RD Sharma are the basic needs for JEE Mains.

You can use NCERT books and previous IIT-JEE question papers and try to solve more MCQs.