Well an icon can be moved or removed from a screen, however that has no effect on messages. Those would have to be deleted directly, have the data or cache of the app cleared or have uninstalled the app they are in.
In regard to the icon, as long as the app was not removed from the device then you should first check that the icon wasn't combined with others to make a folder. Check your other icons and see if they open the app directly or if they open a little folder showing more than one icon in them. If you do find it is in a folder, just 'tap', 'hold' and 'drag' the icon back to the home screen to remove it from the folder.
If it isn't combined with other icons, then you will have to either tap and hold the background of the home screen (to bring up the icons) or slide up on the home screen. Depends on the devices version of Android. Either way, when you see the screen that shows all your icons, then just 'tap', 'hold' and 'drag' the icon back to the home screen.