Is it a good decision to pursue BBA from any college and then prepare for CAT to pursue MBA?

You can refer books such as Logical Reasoning by Arihant, Logical and Analytical Reasoning by Ashok Gupta, A Modern Approach to Logical Reasoning by RS Aggarwal and How To Prepare Logical Reasoning for CAT by Arun Sharma.

Although not many questions are asked from Binary Logic, CAT exam aspirants must not ignore this section during preparation as each mark counts.

There is no specific number of questions asked on Binary Logic in CAT exam. There can be 1-2 standalone questions in Logical Reasoning section of the exam.

To prepare for CAT VARC, candidates must refer How to Prepare for Verbal Ability and Reading Comprehension for CAT by Arun Sharma and Meenakshi Upadhyay and Word Power Made Easy by Norman Lewis along with Wren & Martin High School English Grammar.

FIB is not important for CAT VARC as no direct questions are asked. However, it plays a role in VARC preparation and practice.