NIOS

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.

Not at all, you can easily apply for colleges as a normal student or regular school student, there will be no problems for this situation.

Depends on the college.
Some may accept some may not accept.
So, please go visit the university and get full in more details.
I can't assure you about acceptance, but as per my knowledge some college under Nehu do accept.