CAT

To pursue regular MBA, you will have to appear CAT. In case you still don't wish to appear for it, you can go for part-time MBA which will be a 3 years course but it will have a lesser value compared to regular MBA. Distance learning from Sikkim Manipal or such universities is also an option if u do not wish to appear CAT. Distance learning will be of 2 years but again it doesn't carries the same value as regular MBA would.

It depends upon the number of applicants.

Most of the good colleges have the fee structure in the range of 10-15 lakh rupees. So, it is difficult to get into a good college with your budget.
For more details, kindly refer to the link mentioned below:
https://www.shiksha.com/colleges-accepting-cat-scores-range-70-to-80-percentile-article-11956-1

Start revising the basic maths concepts studied in class 9th and 10th. CAT generally asks questions on profit-loss, statistics, trigonometry, ratio and proportion, basic algebra. Verbal needs practice and same is the case with DI-LR. You can also join a good coaching institute if possible by April/May. Do take weekly tests to evaluate your preparations.
Best of luck.

If you are targeting this year's CAT then you must start the coaching by April/May. 6-7 months of preparation with full dedication and commitment is good enough. Do take weekly tests to evaluate your preparations.
Best of luck.

You can apply for CMAT exam in the third year of your graduation.

You will get an email as to where and when to update your CAT scores.

Can't tell as you have score less in CAT.

Very bleak chances considering your CAT score.