B.Sc

Yes, you can. MBA course only demands a 3-year regular degree with 50% aggregate in your degree. You have done B.Sc. in media science so you can go for MBA in media and entertainment as it has a huge scope and lots of money if you excel.

Both the courses are similar with minor differences in electives. You are advised to choose between them based on the reputation of institute where you get admission. Nowadays, it is difficult to find jobs directly if not placed during campus placement. Therefore, quality of institute is more important than nomenclature of degree.

Hi,
Yes, he is eligible for JEE mains and other exams but there is an rule by CBSE that if you are giving improvement exams then you are not allowed to use previous result anywhere for higher education so kindly consult CBSE for better details and cutoff her name from B.Sc.
I hope you understand.

It is same as BA in journalism. History of media, print media, electronic media production and camera works, communication skills, developmental communication, public relation, etc. are being taught considering B.Sc as a foundation degree.
I would suggest you to pursue BA in journalism, often called Bachelor of journalism and mass communication (BJMC).

You need to have Master's degree to pursue Ph.D. It is beneficial for you to pursue Ph.D from USA.