IIM

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.

Yes, you have a great chance to get into old IIMs considering that your CAT score will be good enough to get the call.

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.

Even the newest IIMs will stand miles ahead of ICFAI.

Hi,
FMS is much better than most IIMs and is quite comparable to the top 3 IIMs.

Hi,
With this CAT score you will not be able to get admission in a top IIMs.
https://www.shiksha.com/articles/understand-the-short-listing-criteria-of-all-iims-blogId-5379

FMS is better as it has a low fee structure with good placement package. The fee structure of MBA in IIMs is very high.

Top MBA institutes in India for information technology are given in the link please check the list:
https://www.shiksha.com/mba/colleges/mba-in-it-systems-colleges-india

Surely there is.
Ask your company to give you educational leave (Depending upon your company's policies) so that you can join the same company after completing your MBA in higher responsibility.