Customized textboxes are saved in an .urm file, which you can copy and load into another game.I play on Windows. The settings for the textboxes gets saved when I import that file to another game, and strangely so does the setting for showing the button, but the position of the button and the colors and opacity of the mod's menu strangely don't get saved. Or maybe I need to restart the game, for the changes to be applied.
Appearance settings you can set globally or only for the current game. When set globally they are automatically transferred to ever other game.