Teaching & Education

No, you must do B.Ed and after that you can apply for M.Ed.

Yes, you can enroll for B.Ed course while working in a school.

Yes, there is an entrance exam to do B.Ed from correspondence like IGNOU, Jamia Milia Islamia etc.

You can write any of the entrance tests conducted by Institutes, and once you clear it with top score, you can get admission into B.Ed from top Institutes.

Yes, you can enroll for B.Ed, as you are a graduate.

You can read this article for your knowledge. https://www.shiksha.com/exams/ctet

That's great that you want to take your career ahead. If you want to do B.Ed course from regular university, then you may apply next year as all universities entrance exams are over now. And, if you want to do from distance learning university, then you can do so now. But, it's better to do this course from regular college because it will be more valuable than doing from Open University. Good universities are DU, Jamia and then IPU. You can search on google as well, you may find many answers of your questions and related questions as well which will give you more clarity about the course and universities.