Is a game based on another game considered a copyright infringement?

The answer will depend upon the country of which you are a citizen. In the US, copyright only protects the expression of an idea and not the idea itself. But without examining both games, it's not possible here to determine if you would be violating copyright laws by releasing your game as it is.

This is very fact dependent. It depends on what you mean by "based on" and what is the same and what is different between the games. You should have an attorney review both games to get a good feel for how you stand.

This would likely fall into the US copyright category of a "derivative work." If a derivative work is substantially similar to the original copyrighted work (the first game) then it would be copyright infringement to proceed unless you first obtained a license from the original copyright owner.