CAT

It would totally depend on you. First of all you should identify your strong areas and your weak areas. This would only be done if you have evaluated your mock tests properly. Remember that the key to crack CAT is SPEED and ACCURACY. Hence it is important that you solve as many questions as possible correctly. And this would only come with practice. Hence in short, practice as much as you can.

CAT exams are more about practice. It is more speed and accuracy than knowledge (unlike JEE). Questions are essentially very easy and if given sufficient time, you will be able to solve all the questions yourself. Hence you should focus more on practice under exam like situations. Post mock tests you should always evaluate what went right and what went wrong. Try to develop an understanding of your strong areas and the weak ones. Improve on weak areas and continue to do well on your strong areas.

I don't think you will receive GDPI call from IIMs with 82 percentile in CAT. You will have to do really well and score atleast 99.5 percentile to get GDPI calls from atleast few older IIMs. Please understand that on an average 2 lakh students appear for CAT and 82 percentile means there are 36,000 students who have scored more marks than you. Seats in all IIMs combined is not more than 2000.

Since you plan to give CAT after three years ,it would be better to now concentrate on your M.Sc & try and score well. Preparation for CAT doesn't require more than 6 months of sincere effort. CAT exams are normally conducted between Nov & Feb ,so one should start preparing 6 months prior to the date of the open test.
Since you plan to pursue MBA after 3 years it is advisable that you pick up a work assignment & gain valuable experience .This work experience will come to your advantage during the campus placement process at MBA

You have to go through internet or buy preparation books.

Hello, the cut off for ILS is usually 90 percentile although college doesn't formally announce the cut offs. After the shortlisting, the selection depends on your performance in gd pi rounds.

Exam Required-CAT 90 %tile | CMAT | XAT 80 %tile
https://www.shiksha.com/mba/course/post-graduate-diploma-management-goa-institute-management/74615

You can refer this link for CAT coaching institute in Tambaram, Chennai:
https://testprep.shiksha.com/mba-entrance-exams-chennai-categorypage-14-47-1-0-0-64-123-2-0-none-1-0

These are some of the best Coaching centers which offer Excellent Coaching for CAT in India :
1.Career Launcher
2. IMS
3. TIME
4. Bulls Eye
5. PT Education
Just check their site out to locate their center in your city.
Know more on https://edudrona.com/right-coaching-institute-mba-entrance-cat-xat-mat-cmat-snap-tiss/?mref=tanu
All the best !

These are some of the coaching centers which offer Excellent Coaching for CAT in India :
1.Career Launcher
2. IMS
3. TIME
4. Bulls Eye
5. PT Education
Just check their site out to locate their center in your city.
All the best !