IIT Preparation

If you have prepared your state board nicely, then 1 year preparation is enough for JEE. Because in JEE, they ask questions form 11th and 12th only. And, you should go through previous years question papers.

It actually doesn't matter in which coaching centre you had been studying in the past as in the end you are the only one who has to seize the opportunity and achieve your goal. However, yes, a valuable guidance should be taken from a right person.

If you have determination and you think you can work hard, then go for a drop. If not, take admission in a college which offers admission without entrance.

Yes, you can appear for IIT JAM.

Sorry to say but its a no as IIT strictly says at least 75% in all subject mean above 75% or 75% not less than it and as you said you are from CBSE, then you won't came in top 20 percentile because top 20 percentile of CBSE is above 85%. So, you try in any other college.
All the best.

Basically, the cutoffs for JEE Advanced exam changes every year. So, just stay tuned. But almost 20 percent is needed in all the subjects.

Yes, if you are able to stay in hostels, Nah, Allen, Resonance in Rajasthan are superb to get superb coaching without stress.

Can I have your question's clarity please? I am not able to understand.

You are aiming for IIT, then you must have to do hard work. Focus on your goal, concentrate on what you learn on daily basis. Practice as much as you can, revise content on regular intervals. Because a year hard work can let you to a bright future. Hopefully, you achieve it.
Best of luck.

The best institute for JEE are FIITJEE, Resonance, Allen and Aakash, you can join one of them or you can do self-study.