Commerce

You may please visit the college personally to get the query solved.

Candidates must have maths as one of their subjects in 10+2 to get eligible for the course.
https://www.shiksha.com/it-software/game-design/course/bca-in-game-development-seamedu-school-of-pro-expressionism-pune-balewadi-231149

For doing architecture you need complete your 12th in science and give an entrance exam.

Yes, you are eligible for this exam. Good luck.

It doesn't depend on a particular stream when you complete a post graduation course rather it depends on your excellence in work so don't worry, if you are skilled then you will surely get hired.

If you have studied mathematics in your class 11th and 12th, then you are eligible to appear for the entrance test of this esteemed institute. However, the courses offered at the UG level are completely mathematical. They offer B.Math and B. Stat degree and not B.Com or BA in Economics.

Candidates should have passed B.Sc with physics as major subject with a minimum of 50% marks in aggregate. Candidates should have a Bachelor's degree in management or commerce from a recognized university with a minimum of 50% marks in aggregate.

Yes, you are eligible to apply for the course mentioned.

No, you will not be eligible for BITSAT as for the entrance, you need to be of Science background with PCM compulsory as this is an engineering entrance. So sorry for you.
Good Luck for the future.