CBSE 10th

https://www.shiksha.com/mba/course/master-of-business-administration-hbs-heritage-business-school-east-calcutta-township-kolkata-114566
Check out this link. They haven't specified MAT for admission, but they do accept CAT and JEMAT.

Hi, you can get college after class 12 th, for pursuing graduation you will get admit in college.
You had to pass 12 th class then after you can go for college.
For more information about college visit shiksha website.

Hi, it depends on your interest. Every field has different scopes. So you choose your stream wisely in which you can score better and had interest in it.
You can go for science because it has a vast scope in future.

It varies from institute to institute. You can visit Shiksha's website for the nearest coaching institute.

Diploma can't get in NIT.

Admit card of class 10th is not required for admission to B.Ed but the certificate is compulsory, so is class 12th certificate.

You have to clear the qualifying exam which is class 12th boards before applying for the UG program.

This depends on your interest and on where you can get admission based on your percentage. Answering an aptitude test for this might help you make your choice. Do a search for aptitude test centers with counselling near you or you could try out an online aptitude test but you will not get any counselling regarding the aptitude test results then.