Kde: how to bind permanently an application to a desktop/activity?

This (and much much more) can be done in advanced settings of KDE's window manager KWin. You can get to it if you right click on window titlebar and select Advanced > Special Application Settings (or Special Window Settings if you would like to apply only to specific window and not all windows of this app). Then on the Size and Position tab you can force it to open on specific virtual desktop or in specific activity (for activities you need KDE software compilation version 4.9, if I remember correctly).

For 4.13.3, you right click on the window title bar and select More Actions -> Special Application Settings. This will open up a dialog with the tab "Size & Position". There will be a check box "Activity" with options to restrict the window to an activity.