M.Ed

Yes you can get admission in M.ed through correspondence without appearing for any entrance exam.
To know about the recognized universities please refer to the link: https://www.shiksha.com/humanities-social-sciences/articles/ugc-approved-distance-education-courses-universities-blogId-13904

If you have completed your B.Ed only then you can pursue M.Ed.

No, you have to complete your B.Ed first only after that you get take admission in M.Ed courses.

The application forms are released in the month of March or April.

For junior college teacher i.e. to teach up to 10+2 you need to have a post graduate degree and M.Ed and for lecturer (the term lecturer is used only for those teaching at graduate level) you do not need to have B.Ed or M.Ed. You need to either qualify SET or NET of UGC. SET is conducted by a state university authorised by UGC and NET by CBSE on behalf of UGC.

English And Foreign Language University
Hyderabad University
BHU
Calcutta university
North Bengal University
Sri Satya Day Institution
Burdwuan University
Kalyani University
Gour Banga University

English and Foreign Languages University, Hyderabad is the best for B.Ed and M.Ed courses.

Yes, it is necessary to have MA degree to pursue M.Ed.