BCA

College change or university change after first year is completely dependent on college and university norms, some university allow it and some won't plus you need to have good scores in first year to apply for the same. For further details contact the college authorities.
Firstly, find out the BCA colleges which allow lateral entry and then proceed further.

Hi,
Pursuing MCA after BCA is not termed as lateral entry. Lateral entry is getting directly into the second year of a particular course. CU has a good reputation, you can think of pursuing MCA from there.

You may pursue the same only after completing maths of 10+2 level if you have not studied maths at BCA level, for this you may opt NIOS on demand exam.

Hi,
As far my knowledge is concern that BCA or any other degree is not required for gaming. All games are programs in some languages like Java, C+, etc. So, if you have the complete knowledge about it and if you are good at programming in these fields then it will be easy to develop any game. As you told that you want to do BCA, if you do this and don't work in programming then it is not easy to develop any Game.
So, work in programming and develop your skills in programming. Then it will be easy to you to develop games.

Dear,
As per UGC guidelines, you can apply for 2 different programmes from 2 different universities in distance and regular mode education.
But choose the regular programme according to your career goal and interest.
All the best!