CAT

Although old IIMs might not accept the scores, there are quite a few B-Schools that accept these scores. Now, most of them accepting this score put more weightage on their GDPI.
Here is the list of colleges:
https://www.shiksha.com/mba/articles/colleges-accepting-cat-scores-range-70-to-80-percentile-blogId-11956

Various coaching classes are
1. T.I.M.E
2. IMS
3. Catking

Top B-Schools in India are:
1. IIM-A
2. FMS
3. XLRI
4. IIM-C
5. IIM-B
6. IIFT-Delhi
7. SP Jain
8. IIM-L
9. JBims
10. MDI
http://www.time4education.com/CAT-MBA/About-MBA/TIME-B-School-Categorisation
You can refer to the link for more B-Schools.

You have a decent chance. Your performance in PI alone does not decide your admission. It also depends on your performance in the WAT round and your overall profile. Since your CAT score is above the cut-off, you might have a chance.

Hi,
For getting admission in IIMs your graduation score should be 60% or above.
CAT score of IIMs closes at 99 percentile itself.
But IIM, Indore and Raipur as tracked in last two academic years take students scoring 96 percentile as well.
It depends on the availability as well.
It is better to target IIM, Lucknow.
Score above 99.4percentile.

Preparation for anything depends on how quickly you learn. There are people who start one year before and some 3 months before the exam date. Personally, for an average student with moderate grasping and commitment towards the test can take 4 to 5 months for proper preparation along with mocks.

Your previous academics are definitely good. However, you seat in IIM's depends on your CAT scores and performance in GD/PI.

Absolutely you will get into top IIMs, provided you score pretty high percentile and able to crack GD/PI with precision.