Do all Fire Emblem games take place in the same world?

The Fire Emblem games are generally not connected, in a similar way that the Zelda games or the Final Fantasy games aren’t. There are some sequels (Path of Radiance => Radiant Dawn), but generally, each game is in its own world.

Does Fire Emblem take place on earth?

The Fire Emblem series does not take place in a singular world. Instead, the stories of Fire Emblem titles comes from various worlds wholly separate from each other.