If you double click a .desktop file on the Desktop, you are asked if you want to execute the script or other options. To disable this confirmation request launch the file manager, open the Preferences screen and enable Don't ask options on launch executable files:

The default Raspberry Pi installation places an LXDE plugin into the panel called updater. This plugin is responsible of the popup which will inform you of eventually package updates available.

You can remove the updater from the panel in the graphical environment, or you can edit the config file /home/pi/.config/lxpanel/LXDE-pi/panels/panel when the LXDE environment is not running.