CBSE 10th

There is no job for IIT after 10th. You can get only very cheap job. For a better job, you should complete graduation.

You can basically choose from science, arts, commerce for +2 or go for a Diploma.
You could choose to go for say engineering, medical, research, if you take science. You can try for CA if you are into commerce. Bank management and law aren't bad either.
Know that if you are determined and dedicated to whatever you choose, you will be rewarded. Choose what you are passionate about or at least what you will enjoy doing.

You can apply for JEE Mains after 12th.

It depends on you and if you have interest in maths then choose maths Science. If you are interested in biology, geology, etc., then choose bio science. If you have interest in social science then choose arts. If you have interest in economics then choose commerce. You may also choose an extra subject.
Best of luck.

Yes, you are eligible to join.

After completing your 10th you should understand which field you want to go for. If you like creating something new or business then fields varies. You can go for science if you want to be a designer, architect or engineer. You can go for commerce if you are interested in business or law. Even if you are interested in history you can go for arts.

Mathematics is the subject which will follow you in your every competitive exam. If you don't like it then it is okay. You can go for commerce after 10th and you can make your career in many fields like law or business.

You can consider Jamia, IPU, AMU UPTU, Thapar, GNDPC-Ludhiana, etc.

You can apply for summer courses, but you will not get admission for UG. You can get that after you finish your ISC or any other equivalent examination.