Colleges in Mumbai

Yes, you can do this Diploma after your 12th from Kazian School of Management, Miraroad (East) Thane and there are other two, which provide online and part time classroom education for this Diploma. The information for these two is given in the below link.
Link- https://www.shiksha.com/accounting-commerce/taxation/colleges/diploma-courses-mumbai-all

Refer to this link
https://law.nmims.edu/docs/student-resource-book-kpmsol-2018-19.pdf.

No, there's no need to give any entrance to get into this college.
You need to have 45% marks in 12th class.
This may help you:
https://www.shiksha.com/business-management-studies/course/bachelor-of-management-studies-vidyalankar-school-of-information-technology-wadala-mumbai-157269

Most MBA colleges allot admission based on entrance test scores. Since you have not appeared for any open test, I am afraid you will not be entitled to get admission for MBA in any good college.

M.A. In advertising and entertainment is really a very nice and interesting course. Here is the syllabus:
Semester 1:
Management- Film
Management- Animation, VFX and Gaming
Management- Events and Live Media
Overview- Broadcast Media
Radio Overview, Production and Business
Semester 2:
Electives (Provided by University)
Semester 3:
Consumer Behavior
Management-Film
Media Planning and Buying
Semester 4:
Electives (Provided by University)
Another thing is, this course is provided by SK Somaiya College, not KJ Somaiya, so here is your course structure, read it and then choose wisely.

Hi,
Please specify which college you are talking about as it might be difficult for you to complete your graduation but, it is not impossible.