BITSAT

Check the link below:
https://www.getentrance.com/engineering-entrance-exams.html

There is not a defined line that you have to read a certain author's books to clear an examination, go with the author or publication that suits your learning style and which you find easy to understand.

Only two attempts, the year that you have completed your 12th and the next year.

Hello,
Almost all of these entrance exams are conducted with aim of testing student's ability of logical thinking and knowledge of fundamentals of science. I would therefore advise you to stick to brushing up your basics. Besides, you will have to learn to answer in stipulated time. There are practice papers available, you can try these. But, get answers vetted by your professors.
Best of luck.

Syllabus of both EAMCET and BITSAT is similar to JEE Mains.

EAMCET and BITSAT are totally different exams. In BITSAT, English and logical reasoning is included and EAMCET is very easy as compared to it. BITSAT and JEE Mains exam is of same level.

Yes, you will get admission in ICFAI University.

The books of Arihant Publication are the best for BITSAT preparation.

Syllabus of IIT JEE and BITS is same but in BITS you have to prepare for English. Also, the level of BITS is higher than that of JEE Mains and 12th board but low in comparison to JEE Advanced. I think you should first focus on JEE Advanced so can you will be able to solve good quality questions and able to clear both BITS as well as JEE Advanced
Best of luck.

No. In BITSAT, class 12th marks are not given any weight-age.
You need to score well in BITSAT to get admission in BITs, Pilani.