Is there a way to drag and drop program shortcuts to the desktop in Ubuntu 19.04

Solution 1:

In Ubuntu 19.04, like in previous Ubuntu versions, it is not possible to drag applications from the dash or the application menu to the desktop.

Desktop files from Ubuntu 19.04 onwards are handled by a Gnome Shell extension, and not anymore by files. You can still copy or create .desktop files on the desktop as before. The right-click menu has an option "allow launching" to turn that .desktop file into a launcher.