MBA Entrance Exam

Sorry, but CAT exams are for Masters in Business Administration. So, before you do it you should have to complete Bacholer's degree or any equivalent course. After Diploma, you can't apply for CAT.

No. CAT is one way to get in MBA colleges. You can give MAT XAT GMAT ATMA CMAT IIFT NMAT etc. Many options are there. Don't limit your options only to CAT.

Go for online class options. You can see whenever you want and can study from wherever you want. With an ease. And can clear doubt from n no of videos and you can do it for free or paid also. See as much as YouTube video of different professors for your CAT preparations. All the luck to you.

Your graduation score is a bit less, I would thus recommend you to try for a very high percentile - in the high 90's to stand a chance.

Only the latest year's CAT score is considered for admissions, you need to appear for CAT in the very same year in order to apply for admissions.

Start by solving Maths problems given in previous CAT exams (You can find books containing the same).
The rest can be covered easily while preparing from an institute.

You should aim for at least 99.5 percentile otherwise chances are bleak.