CAT

It will be very difficult to get a call from Alliance University bangalore. Infact at your score it will be very difficult to get a good college. I would suggest you to prepare better for other upcoming management exams such as CMAT, MAT and ATMA.

You can go for an executive management programme if you have work experience of more than 3 years. There are some very good colleges offering Executive 1-year MBA. Great Lakes, Chennai require minimum 2 years of work experience, same goes with ISB Hyderabad, Welingkar Mumbai, KJ Somaiya, IIMs and SP Jain.

For the score you have you can apply to colleges like K J Somaiya, AIMS Bangalore, Welingkar, ABBS would be a good try. Try for BITS Pilani and S.P. Jain if their cut off is low.

You have chances of getting calls from IIT (Kanpur, Madras, Roorkee and Kharagpur). You can also apply for colleges like TAPMI, LBS-Delhi, K J Somaiya, BIM-Trichy and IMI-Delhi.

Yes, you are eligible as many of the colleges accept this score. Don't worry you can easily get admission in any of the college depending upon the location you prefer.

No, only CET for MMS, the cut-off being 99.01%.

No, work experience is not compulsory. However, a couple of IIMs give extra points to students with work ex.
Regarding preparations, the earlier you start the better it is since there are a lot of things that come with practice. You should at least give 8-12 months for a proper preparation and join a test series for sure. TIME coaching has a good test series. It starts around 4-5 months before the CAT date.

Since you graduation grades are little low, I guess you might not get a call from IIM-C and IIM-B. But, apart from that you can expect a call from most of the old IIMs and new IIMs.

To be honest, no college will take you with this percentile but if you are from reserved category then you might have chances of getting admission in some good college.

The best coaching center for CAT preparations is undoubtedly TIME. I don't think there is any other better coaching institute other than this, go for it.