CAT

CAT is a test conducted by IIM.
MAT is a test conducted by AIMA.
CMAT is a test conducted by AICTE.
You can also pursue MBA after qualifying XAT or GMAT exam.
All these exams have different modules or pattern of questions.

It will be better to have dedicated preparations for CAT in the year in which you planning to appear for CAT. However, you may work to continuously improve your numerical, data interpretation and verbal communication ability along with your graduation study to improve your chances to crack CAT.

You need at least 90%. This is the least for getting a good call. For converting and making into a good IIM, you need 90+ percentile

you need to score >99% ile.

you need to score >99% ile.

Every college has its own cutoff. Top colleges require 70 to 80 percentile.

Kindly visit the links mentioned below:
http://www.oldquestionpapers.net/2010/06/10-year-cat-question-papers-solved-free-download-pdf.html

If you are not going to join any classes, then you can join online mock tests of 3 to 4 classes. You should analyze your strengths and weaknesses after every test. You need to work on your weaknesses. You should improve your scores after every test.

Jamshedpur is certainly good.

There are a number of coaching centers among them Career launcher, TIME and IMS are reputed ones. Since you are in Patna, you can prepare there as well. Patna is a hub for coaching and you can find a number of institutes in Ramna Road, Kankadbagh and Bhikna Pahadi area.