CBSE 12th

Yes, the basic eligibility criterion is:
Candidates should have passed or appeared in Class XII final exam in any discipline from a recognised board, university or council.

B.Sc and B.Tech both are good courses for you. But in B.Tech, maximum universities ask for 45-50% marks in PCM. So you have to check before trying for some university. But in B.Sc, there is no percentage criteria. There are lots of degree colleges in Haryana, India which are providing B.Sc course. Other than it, you may also choose BBA for further studies.

Almost all the seats are filled and there are very less chances to get admission because the session has started. But you can try by contacting the concerned authority. Ask them if there are any seats vacant in their college.

Yes, you can do this course.
Eligibility:
Bachelor of Arts [BA] (Music Vocal) is a 3 year undergraduate full-time musical course, eligibility to which is 10+2 or an equivalent examination from recognized university. Candidates should get a minimum average of 50% marks in 10+2 examination (5% reduction for SC/ST/OBC students).

You should prepare for next compartment exam.

Yes, there are Diploma courses available. Mention your Stream or in which field you want to go.

Other than Bachelor's Degree, there are many Diploma Management courses are available after class 12th:
I have listed some Diploma management courses below:-
>Diploma in Hotel Management. >Diploma in Marketing and advertising. >Diploma in event management. >Diploma in travel and tourism management. >Diploma in Retail management.

Yes, you can apply for the History (H), but the admission is based on the marks obtained in 10+2, means if any student has more marks than you, then he can get admission first.

Kindly go through the following link:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjPs-iFqpTcAhWMRY8KHariB-kQFjAAegQIBBAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H.

Kindly go through the following link:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjPs-iFqpTcAhWMRY8KHariB-kQFjAAegQIBBAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H.