If they're shortcuts, the arrow is part of the shortcut. You can't remove it. But you can use the Change Icons feature to select a different icon for the function or location.
To remove unused items from the desktop in Windows, a user can use the Desktop Cleanup Wizard, located in Control Panel > Appearances and Themes > Display.
To remove the shortcut arrow from desktop icons in Windows, you can modify the registry. Open the Registry Editor by typing "regedit" in the Run dialog (Win + R). Navigate to HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\Shell Icons, and if it doesn't exist, create a new key called "Shell Icons." Create a new string value named "29" and set its data to an empty string to remove the arrow. Restart your computer for the changes to take effect. Always back up the registry before making changes.
Did you try right clicking on your desktop and choosing "arrange icons with" and then choosing "show desktop icons"
Right Click Your Desktop Select View Untick Show Desktop Icons
Aside from manually deleting the shortcuts and icons on your desktop (the Recycle Bin cannot be deleted): you can right-click the background, find "Arrange Icons By" and press "Show Desktop Icons". This'll hide all the existing icons, so if you press "Show Desktop Icons again, they'll all return.
You right click on the icon, then click delete, then click Yes
If there is no space on the desktop for icons, the icons will run off the screen. Thus the icons will not be displayed. If you use up the space, you could delete icons you don't use, resize the icons, increase the screen resolution, or create a folder on the desktop to move your less commonly used icons to.
in my opinion the icons are stored on the desktop
Don't know if you are talking about any specific application but to view desktop icons, right click on desktop go to 'view' and select/check (if unchecked) 'show desktop icons'.
your screen refreshes when you close a program causing your desktop icons to flicker
Right click on an empty space on the desktop, go to "View" & click on "Small Icons"
Right click on desktop go to 'view' option and there you will see 'show desktop icons', select that and icons should appear.