Exam

Since you have got 50 marks in maths you must take the improvement exams to eradicate any job oriented problem or any related stuff in future. You must secure a minimum of 60% in each subject.

With this score I don't think you could get any good MBA college for MMS.
Try next year.
But you can apply for PGDM in some good colleges.
Your CAT Percentile 65 is good. So, apply with your CAT percentile.

You may try in some institutes other than IITs which accepts advance scores like IISC0Bangalore, IISER, IIPE, IISST, RGIPT, etc.

CAT stands for Common Admission Test and MAT stands for Management Aptitude Test. They are entrance exams for MBA.

Yes, you can get admission in the same but you have less chances for CS in the main campus.

All institute who take admission through GATE scores are not providing stipend however all NITs , IITs, IIITs and most government engineering colleges provide stipend. For more detail you may go through institute website and contact them by finding contact information.

To get into IITs you must secure above 110 marks in JEE Advance.

To crack IITs you should have full command on NCERT books. You can also refer RD Sharma, Arihant and RS Agarwal.

There is no specific Hindi medium coaching for JEE. You will be provided with a blend of Hindi and English. Some of the best coaching institutes in India are Allen, Resonance, Rao IIT Academy, Akash, etc.