NIOS

As NIOS is a valid and recognized board of education and is equivalent to other national and state education boards. If you have satisfied the eligibility criteria posted by MNCs, then the NIOS certificate will not affect your placements.

The student passed from NIOS board can appear in any Medical entrance examination, engineering entrance examination and even in NDA Entrance exam. No University/Institution in India can question the authenticity of NIOS board.

Yes, you are eligible for B.A. Courses at SJC Bangalore. The eligibility criteria is given below. Eligibility : A candidate who has passed two year PUC examination of Karnataka State with any combination of optional subjects or any other examination from recognised Board/University or through National Institute of Open Schooling (NIOS) recognised as equivalent thereto shall be eligible for admission to B.A. Course.

As you did your 12th from NIOS, if you are passed in 5 main subjects then will be considered pass irrespective of the fact that he/ she fails in 6th /optional subject. So first confirm that you are pass in 5 main subjects or not.

Yes, NIOS board's students can apply for English honors.
Good luck.

Yes, you can do Master's degree regular after completing B.Sc.
Good luck.

Yes, you can learn music in your graduation for sure, doesn't matter which board you gave.

Yes, it does accept NIOS, you will have to get an equivalent letter or approval from the state board or something, like eligibility or NOC certificate.