New
#1
First thing I'd do is right-click the desktop/screen, choose View and pick something to change how the icons are lined up, especially if you can't add something to a different place like in the middle of the screen. Maybe turning the icons off then back on will refresh its 'mind'.
But it stops happening when I set icons to medium not small, but medium is too large for me...
What is your screen resolution? Also, have you customized things to where text and icons are not at default, maybe 125% or 150%?
Right click in the center of that red box you drew. Does the right click menu look like it has a "Delete" selection? If so, press the Delete with your mouse and see what ends up in the trash can.
Or right click in an empty space on the Desktop > View > uncheck Auto arrange items if it's checked.