CAT

CAT score is accepted across most of the colleges in India unlike UPSEE which is accepted mostly in UP. As these exams are just entrance exams and your performance would only decide your final placement, I would refrain from commenting in this regard. But just for your information by performing exceedingly well in CAT you can get into IIM A/B/C which are among the best management schools in India.

I would not be able to clarify your question regarding IIM L, but for IIM A, converts usually have 94-95+ percentile.

In my opinion, CAT is better because no. of colleges accepting CAT scores are slightly more than accepting CMAT. But there is hardly much difference.

CAT selection: https://www.shiksha.com/mba/exams/cat
IIMs selection: https://www.shiksha.com/articles/understand-the-short-listing-criteria-of-all-iims-blogId-5379

You can surely apply for BMS ( Bachelors of Management Studies). You can pursue your CAT studies along with studying BMS and the college even provides guidance for the same. BMS is very close to BBA yet is very different and a new course.

Generally, it depends on the fact that how strong are your basics I.e till 10th. Mathematics and all.
If that's fine and you believe you are strong in basics.
You can have some time for you.
Else, it is suggested that you may join in the first year itself.
mostly students tend to join it by the end of 2nd year or 3rd year starting.
Anyway. there no set rule for this.
But it is good that you join it.
The earlier the better.

Hello Shubham,
Not at all, you need not worry about it. During the campus selection, companies give more importance to your interview process, overall performance (academic + Extra-curricular) during your two years' MBA program and your MBA entrance exam(s) and past academic scores (10th, 12th & B Com), rather than seeing which was your graduation degree.

Hello Sourav! https://www.shiksha.com/mba/articles/colleges-accepting-cat-scores-range-70-to-80-percentile-blogId-11956 Kindly visit this link to know the B-schools accepting CAT score between 70 and 80 percentile.