CAT

There are three big players for CAT coaching in Indore, TIME, CL and CH-EM. From my personal experience and talking to my friends who joined one of these coachings, TIME is better than other two (specifically talking about Indore). Though you may probably need a CL/IMS test series along to really taste the CAT. That's because level of coaching at TIME is way above the level of CAT. CL and IMS are closer.
Regards.

With this score and academic background you are eligible for Christ University.

You can ask CAT related doubts on Shiksha Ask and Answer Platform. You will get the apt solution for your query.

You can't do MBA after your 12th. You need a suitable degree before doing any Masters. So, check for colleges to do your BBA or engineering or any other management degree if possible.

https://www.quora.com/How-did-99+-percentile-prepare-for-CAT
You can find tips regarding the preparation for CAT. You will have to purchase the model test papers as they aren't available online. You can go to Flipkart or Amazon and buy the complete book.

Percentile refers to the score that is allotted to an individual basis the performance of the total number of students appearing for the exam. Percentile is followed in all major competitive programs to rank students based on their performance in comparison to the others appearing for it.

96+ overall is required for getting calls from baby and new IIMs (sectional must be above 80 percentile). For older IIMs 98+ percentile and a really great GD/PI will do the trick.

Yes, definitely, you have a chance to get a call from IIMs, provided you do well in CAT. For a better idea, you can visit the website of IIM and can check out about the weightage each IIM gives to these components, as each IIM gives different weightage to your past academic record.

Till now, no IIM provides an MBA degree, especially in hospital administration. There are other colleges in India like GIM where you can opt for the same.