Is there a way to delete saved games permanently? I keep getting the saved games I delete showing up when I start the game? i.e. the next day. Thank you

I presume you're using Galaxy and cloud sync. In that case, while the game and Galaxy are open, go to the Save/Load screen and select any saves you don't want and press 'Delete'. this will delete the saves. Now quit the game and Galaxy will sync what you have left. Alternatively, you can delete them from Windows Explorer while the game and Galaxy are open... same result when you quit the game.