Distance/Correspondence

Yes. There are universities which provides distance LLB to students. IGNOU is one such examples.

You have sufficient educational qualifications to apply for jobs on PSU, Government and Private sector.

You can do a MBA in hospital administration.

In correspondence course, the student has to rely on their own learning skills and self learning material provided by the university/institute they may be enrolled with. A Distance learning course allows for more interaction with a guide. It is structured such that a student can learn at their own pace.

Hey Vishnu,
There are many number of people who pursue MBA. So, to have a difference from others please go for a full time course with good CAT score.

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

Yes, you can pursue both the courses simultaneously.

IGNOU is the best. You can try for the admission.

You can do a MAJMC course for this field.

Switching from a regular to correspondence course might not be permitted. You may have to quit your B.Sc. course from DU and then take up a correspondence course starting from first year. If you have been selected in the Navy, I would advise you to prepare for starting with them.