CAT

No problem, you will be eligible to do MBA. Your UG graduation is enough to join in Management in Sathyabama University.

Dear Debmalya,
No Working with NGO wouldn't be considered as work experience when you will go for admission in business schools, though the gap of 2years won't affect your chances of admission.
Business schools ask for justification if gap is of 3 years or more,
All the very best

Cutoff for CET is 99.2X percentile and for CMAT is 99.9X percentile.

I recommend anything above 95 will land you to premier B-School, On safer side you need 90 minimum so you can get top 30bschools. Also a good GDPI score will land you with low entrance exam score.

You need to prepare for CAT exam from TIME, IMS coaching when you are in the third year. You find difficulties in solving CAT papers of previous years, you need the help of Arun Sharma CAT books , and you must study your papers in graduation. You just need four hours to seven hours a day for CAT study. Best of luck.

for time it is around 40,000

It is 99.99 percentile.

There is no fixed answer to this. However you are seriously disadvantaged in terms of your percentages. To make up for that you will have to score really well in CAT. In my personal experience you will need at least 99.7 - 99.8 percentile overall. However the criteria to compute composite score changes every year and also the scoring depends on the incoming batch. But in general with 99.7-99.8 percentile you should get more than one call from IIMs.

Go for CAT exam in my opinion. It'll open many job opportunities after completing your MBA. Don't afraid of English. Start reading Times of India and Economic Times and take down the difficult words and their meanings in your notebook. It'll improve your English. MBA gives you more exposure. Best of luck !

Some of best institutions of the country accepting CAT/ MAT/ XAT/ CMAT/ GMAT are
1. IIM Ahmadabad/ Bangalore/ Kolkata
2. IBS Hydrabad/ Mohali
3. Lovely Professional University, Punjab
4. NMIMS, Mumbai
5. ISM, Dhanbad
6. Great Lakes Institute, Chennai
7. AIMS, Bangalore
8. Kirloskar Institute, Pune
9. Pune University
10. UPES, Dehradun
Check their websites for more details.
Good luck.