CAT

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.

Yes, you are eligible. Apply before the deadline.
All the best!

Since admission is based on other parameters too, you may apply.

With this score, certainly no. However, you can always try next year. Good luck.

Yes. It's enough to get a call but you have deal with great performance in group discussion and also in your personal interview which is conducted by the college.

Yes, you can get a call.

IFMR, ITM-Mumbai, Great Lakes are the good colleges you can try for.