CAT

No, it is not at all necessary. Self study is all that matters. But take mock tets daily. Here are some good books which can be used for CAT preparation :
1.How to prepare for Data Interpretation for the CAT   TMH / Arun Sharma
2.Pearson Guide to Quantitative Aptitude and Data Intrepretation for CAT by Nishit Sinha
3.Quantum CAT by Sarvesh Verma
Know more about CAT on :
https://edudrona.com/common-admission-test-cat/#1464927769900-a0617f54-da37/?mref=tanu

Start self study. The areas which you need to work on to excel in CAT are you logical reasoning skills, Vocabulary skills, Mathematical Skills ,Quantitative and Qualitative Analysis Skills and conversation skill.
Some of the Books recommended for CAT are-
1.How to prepare for Data Interpretation for the CAT   TMH / Arun Sharma
2.Pearson Guide to Quantitative Aptitude and Data Intrepretation for CAT by Nishit Sinha
3.Quantum CAT by Sarvesh Verma
Know more about CAT on :
https://edudrona.com/common-admission-test-cat/#1464927769900-a0617f54-da37/?mref=tanu

There is no official document which states the fact. If you consider for the interview purposes, maybe some people might have a bias. But the interviewers of IIMs are experienced enough to not let these biases affect the decision making.

I will like to share IIM students tips. Go through this once. This is very helpful for me. And definitely helpful to you also.
http://www.mbaonemi.com/articles/entrance-exam/iim-students-share-tips-cracking-cat-exam/

yes. it is possible to get admissions. in private university they are gona take GD AND PI round and based on Your this test uh can get admisons

I suggest you write a mock CAT to figure out your strengths and weak areas. Depending on your score you can figure out when to start preparing. Its possible to score well in CAT by preparing rigorously for 4-5 months if your basics are good.
Check this link to know more about CAT :
https://edudrona.com/common-admission-test-cat/#1464927769900-a0617f54-da37/?mref=tanu

According to me : you should write a mock CAT to figure out your strengths and weak areas. Depending on your score you can figure out when to start preparing. Its possible to score well in CAT by preparing rigorously for 4-5 months if your basics are good.
Know more about CAT at :
https://edudrona.com/common-admission-test-cat/#1464927769900-a0617f54-da37/?mref=tanu

I would suggest that you write a mock CAT to figure out your strengths and weak areas. Depending on your score you can figure out when to start preparing. Its possible to score well in CAT by preparing rigorously for 4-5 months if your basics are good.
Know more about CAT at :
https://edudrona.com/common-admission-test-cat/#1464927769900-a0617f54-da37/?mref=tanu