IIT

There is no separate examination conducted by IIT madras, enrolment in IIT madras is done through JEE advance and its one of the toughest engineering examination across India

allen or resonance or vibrant all threes are good

Don't panic! If I assume you are in +1,then you have ample time. don't worry. Start from the basics of the subject and make yourself strong. Follow HC Verma or DC Pandey and make sure you solve maximum of the problems atleast from HCVerma. As I said you must make your basics strong coz when you go to +2 there is a more chance of forgetting the concepts. So "FOLLOW THOSE BOOKS - SOLVE PROBLEMS - REVISE BEFORE +2 DURING HOLIDAYS ONCE ". Moreover make yourself more stronger in Maths & Chemistry.

yes the course is same.

IIT offers dual degree after 12th that is B.Tech plus M.tech and the total duration is 5 years , you need to have minimum 75% in class 12th or you should lie in top 20 percentile of your respective board in 12th to get into IIT

Chandigarh university is best.

Can you be more specific in your question ?

mostly b. tech persue the degree of IIT-JEE and Other Engg- exam so you can try for that.