Distance/Correspondence B.Sc

Please use the link provided below for a list of colleges which offer courses in B.Sc nursing (correspondence) in Mumbai. You can use the filters on the webpage to navigate to a college of your choice.
https://www.shiksha.com/science/colleges/distance-correspondence-b-sc-colleges-mumbai-all

Please visit the official website of IGNOU regularly for admission notifications. For more information regarding eligibility and selection process, visit the following links:
https://www.shiksha.com/medicine-health-sciences/paramedical/course/b-sc-hons-in-optometry-and-ophthalmic-techniques-indira-gandhi-national-open-university-saket-delhi-83915
http://www.ignou.ac.in/ignou/aboutignou/school/sohs/programmes/detail/204/2
http://www.ignou.ac.in/ignou/aboutignou/school/sohs/programmes/detail/204/2
All the best.

Do B.Ed and start preparing for TET, this will lead you to a teaching job.

Please refer to the link provided below for details on getting admission in Punjab University. You would be able to select a course of your choice and its mode:
https://www.shiksha.com/university/panjab-university-chandigarh-4026

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.

No, you cannot pursue B.Sc in IT in private mode.