CAT

If you have basic ability you can crack CAT with one year of self preparation.

Although there hasn't been an official confirmation on this, but following the previous year trends, CAT'16 is most likely to be held in the month of November'16.
So, that gives you roughly 9 months for preparation, if you are going to write CAT'16. For a month-wise preparation methodology for CAT'16.
All The Best.

Your academic performance looks impressive and in my opinion you should get a GD/PI call from IIMA if you secure more than 99 percentile.

I am not sure as you would be borderline case for all IIMs and other top colleges. And also as soon as results are out, shortlists are announced. Hence you should not worry about the interview calls. I would suggest you to focus on the CAT and do your best.

It depends on what package you take as its Your ability to cope up with the syllabus. Generally it can be 3 months to 15 months.

Dont know about CAT, but JEE and NATA are the scores accepted by many university, some accept JEE, and some NATA only.

Yes, you are totally eligible. But the CAT exam scores will be accepted for the next year batch if you have appeared CAT this year.

Yes you can, there are online coaching available so look for classes from Byju's, Mbaguru etc.