Science

No, it's not possible because it is a required criteria to pass in PCM with 60% marks. You may give class 12th exams again or go for any other options.

Yes it's a very good option for a better career. But only if you can live away from your family and are adventurous

Yes, you can get admission in BBA after completing your class 12th. You have to give entrance exams for BBA after which you can take admission in colleges for BBA. Any stream student can pursue this course.

Dear Apoorva,
There is no such course as MBA game design, the degree that you can pursue is Masters in game design. And you can pursue the same after B.Sc visual communication.

Yes, you can very well go for BA after science in 12th. Check the below link for colleges offering BBA-
https://www.shiksha.com/bba/colleges/bba-colleges-delhi-ncr

Manipal is one of the known institutes you can look for. You can compare the colleges on below link based on rank/placement/fees.
https://www.shiksha.com/science/colleges/biotechnology-colleges-karnataka

Dear
According to your query you can consider these options
Maths/Stats hons
Economics hons
Actuarial science
B.com-finance & Accounting
Bachelor of Finance & Investment analysis
BBA-Finance & accounting, International Business
CA/CS
Apart from these field you can think of these fields too
BBA LLB/ B.Com LLB
International Relations
Journalism
BCA / B.Sc-IT
English hons
Psychology
So choose the programme according to your caliber and interest.
All the best

Maths syllabus is not tough in BCA. Any average student can clear it with minimum effort. All the best!