CAT

I think you can take admission in the college with CAT score, but for more clarifications about admission via management quota, kindly get in touch with the college officials as they are the right party to answer.

Candidates having even 90 percentile in CAT are not getting best colleges, because the competition is very tough. With 30 percentile, you will be getting grade B or even lower colleges.

It would be better if you wait for CMAT, as you can get better college.

It is not compulsory to appear for CAT to get into UBS but it is mandatory to appear for at least one entrance test (NMAT, GMAT CET, etc.)
But, if you listen to me, go for CAT there's a lot of learning from the coaching classes such as TIMES.

Hi dear,
CAT acts as a qualification test. Scores are secondary if you are not aiming for IIMs and top B schools.
At UBS, a Telephonic interview will be conducted and if you perform well plus your academic scores are better, you may get selected here.
But, before you plan to admit yourself into UBS, don't forget to visit the campus at first.

Your percentile is quite good, so you can try in some of the private universities, which offer MBA programme by contacting them, such as KIIT, GLA, LPU, etc., but you will have to appear for their entrance exams.

Yes, but you will have to appear for the entrance exams of that respective university or college in which you are willing to get admitted. Universities like KIIT, GLA, LPU, etc. Conduct their own entrance exams, so you can apply for them.

Being general candidate is a tough job. But, the profile is strong too. Visit this link to get a prediction https://www.shiksha.com/mba/resources/iim-call-predictor.

The expected cut-off this year will be up and above 80 percentile and it varies according to the applicants year after year. I would say you have very little chance of getting a call. All the best!