Can I transfer my old save game to the new version? If so, how do I do it?! By the way, I'm playing on an Android device

1. Do not Uninstall the game.
2. Download the latest version of the game.
3. Install the latest version just like when you first Install this game, it should say "Update" instead of "Install" (But if it say "Install" instead, just install it.)
4. Done.

As long as you didn't Delete the game or Uninstall the game, your save files should be intact.