Distance/Correspondence

The main aim of NTT course is to cater to the nursery (pre-primary) level teacher workforce in India. NTT students are trained in areas like child education, teaching methodology, nursery level subjects & communication. The training turns 10+2 passed students into skilled nursery teachers.
Pursuing NTT from distance learning wouldn't make any sense, as that would not let you learn a lot of things. In India, it is perceived that distance education doesn't make you competent enough. So, I would suggest you pursue a regular course instead of distance learning.

You may please visit the official website of National Institute of Business Management (NIBM Global). National Institute of Business Management (NIBM Global) offers one year MBA, two years MBA and one year Executive MBA training for working professionals and it also provides online video tutorials to all its registered students. NIBM training programs help students as a learning aid while they pursue the actual MBA.

Yes, you can because you are a graduate now.

Please refer to the link provided below for a list of colleges which offer distance courses in medical from India. Additionally, you can download their brochures which contains important information regarding course eligibility, admission dates, application form availability, etc.
https://www.shiksha.com/humanities-social-sciences/articles/ugc-approved-distance-education-courses-universities-blogId-13904

Sorry in Annamalai University, they will not grant you admission if you have not completed 10+2.
As per NCTE norms, regular teachers working in primary, middle, secondary or higher secondary schools in Tamilnadu, recognized by State / Central government, with a minimum of two years teaching experience are only eligible for admission into Annamalai University Distance Education B.Ed course.

What are your subjects?