Because there may be more than one activity, what is the role of the ~/Desktop folder ?

Is its content displayed by a widget that can be added to every activity?

In one activity, adding a link to the desktop from the launch menu created a .desktop file in ~/Desktop,
in another activity, the file was created in .local/share/applications.

What is the system behind these placements?

This is under OpenSuse 13.2.

The ~/Desktop folder is the location that was traditionally displayed on the desktop (ie. the files in there appeared in the desktop) and is afair the default location for the folder view plasmoid.

Desktop services belong into the corresponding XDG directory, for local (a particular user) installations that's usually .local/share/applications.
If it's only on the desktop, but not the XDG directory, the application won't show up in any launchers/startmenus.

Nasty applications spam their icons onto the desktop just as they do on windows - complain to the developer.
This has absolutely nothing to do with activities.

Thank you.

Which activities display the Desktop folder then? Because here there is one that I can clone that does, all the other I create don't.

The other activities, where I drag icons onto their desktop, in which folder or file is their desktop configuration stored?

This has nothing to do with activities.

Plasma has different desktop "containments" - one's "just" a wallpaper where you can add random plasmoids (such as the folderview) and the other is the rather "traditional" (concept popularized w/ Win95) iconview, where the entire desktop is a folder view.

You can have either in as many activities as you wish.
Rightclick the desktop and select "Default Desktop Settings"
In the dialog that pops up, "unlock widgets" (if they're currently locked) and as "Layout" choose "Folder". Then hit apply.
The rightclick menu of the folder layout allows you to choose a directory to disply (eg. ~/Desktop, but could also be ~/MyPictures or so)

PS: the "icons" on the "Default" desktop layout are actually plasmoids - they're afak configured in the ~/.kde/share/config/plasma-desktop*rc config files.
I suggest to not edit those by hand unless you know what you're doing.

Thank you, that clarified everything.