CAT

Yes, its worth every penny. The level of faculty, interaction with peer group and learning is unparalleled in India. Hence, its worth it.
Do understand that unlike other government institutes (read IITs/NITs), IIM's do not take any form of monetary support from government. Hence, the complete expense of the education is born by the students itself rather than the tax-payers of India.

You can start preparing diligently for CAT. If you do not have much idea about CAT, I would suggest you to join a coaching institute with good faculty to help you get the basics right in DILR/Verbal/Quant. After the basics the next challenge is to solve the said question within a stipulated time. Hence, second stage of your preparation should deal with giving mocks and analyzing your mistake repeatedly till CAT.

Good chances, you are a good candidate for MBA in finance. Prepare well.

Since you have completed a 3-year degree in 5 years, I am assuming you have not-that-great academics. If that's the case then getting admission to IIM-A will be difficult even after getting a high percentile as IIM-A gives substantial weightage to academics.

Hi,
A common question troubling MBA aspirants now-a-days is when to commence with CAT preparation. Some of the questions we encountered on the web are:
Is it ok to start preparation in June? OR
What is the best time to start CAT preparation?
So the right time to start preparing for CAT is four-five months before the commencement of exam.
https://www.shiksha.com/what-is-the-best-time-to-start-cat-2015-preparation-article-10892-1
All the best.

Hi,
Other than B.Tech, you can opt for BBA in graduation.
All the best.

Get a clear idea of what the syllabus is. I hope you know that the exam consists of Quant, LR/DI, and English. Start practising. There are a lot of books available. Give time to all the four and to get an idea of the difficulty level of each, solve the previous years CAT questions. You can choose to take the test series of any coaching institute, later, if you think you need it.

You can try for MAT and if you get a good score, then you can go for CAT exam.

Hi Vikash,
Normally, IIMs will close their admissions in between 90 to 99.99 percentile. The other private business schools and IITs MBAs close their admissions in between 85 to 93 percentile.
All the best.

No such cut-off is declared.