MBA Entrance Exam

Nope! CAT score is accepted all over the india only for management studies!
Good luck!

CAT is accepted by almost all the B-schools in India and most popular exam for MBA! CAT is harder to crack than MAT. Good luck!

Visit the link given below to get full information about the pattern of the CAT:-
https://www.shiksha.com/mba/cat-exam-pattern
CAT is difficult due to high competition, advance aptitude, Reservation, Admission criteria!
Good Luck!

No, it is not compulsory to join a coaching for any Exam! You can prepare yourself, just believe on you, make a goal, be dedicated and focus on each term!
But, if anyone helps you and guides you to reach the goal then it's not a bad idea! Coaching works as a coach in your life they give you the direction and In coaching you will meet new peoples and compete with them, This improves your skills!
Good Luck!

IIM not only focus on the CAT aspects. It focuses on the all aspects such as CAT score, 10th, 12th, graduation marks, gender diversity, experience, GD, PI.
Good Luck!

They are both tough and different kinds of exams.

You can join TIMES, Career Launcher, IMS, etc.

Almost the syllabus is same! The difference is difficulty of questions! CAT questions is more difficult than other!
Good Luck!

Some people find 4-6 months and some 12 months, its depends. But certainly this is largely depends upon person to person.

Identify your strength and weaknesses. Make sure you practice more on your weaknesses more and also do not leave your strengths aside. You keep giving less hours on your strength and more hours on your weaknesses. Also keep on practising model papers and keep time yourself for each section as time is an important factor in CAT.