No, I haven't locked my widgets. I can move them around freely, I can create them, I can delete them. But I can't resize them and I can't get to their handles.
I searched in here, and found two answers, which did not help. So, I did 'tweak' the widgets in DesktopSettings, to no avail. I did an 'unlock' whereever I could have done one (though none was locked).
The locks looks like a horizontal eight, in black, barely visible on the lower left side of each icon.
I run kubuntu 18.04, daily updated.
The first image shows the lock (?) across the icon. The second image shows some widgets that are open for editing, and some, with names in italics, that cannot be modified.
I'll only address the desktop icon issue here.
Let's say you drag a .desktop file from /usr/share/applications to your Desktop surface. When you release the mouse, you'll see a small window with the following options (among others):
If you choose Copy Here, the text for the resulting icon will be normal and there won't be what you refer to as a "lock" sign. But there maybe an exclamation mark indicating that you need to right-click on the icon and change its permission to Executable. Now, if you double-click the icon, the respective application will launch. Such a desktop icon can be further edited.
If you choose Link Here, your desktop icon will have italic text, the lock symbol and can't be edited. But you won't need to change any permissions. This is because what you've done is to create a symbolic link. And in Kubuntu, symbolic links are shown in italics.