Problem 1 - I do not have that icon (pinephone speaker). In general - application launchers are taken from /usr/share/applications (system ones) and from /home/"yourusername"/.local/share/applications (user ones). Removing corresponding .desktop file removes also the entry at desktop. The most correct way of removing them is to uninstall the application...
Problem 2 - I have learned that it is better not to mess with desktop widgets icons etc. So I have just that Phone and Phonebook icons and that's all. From time to time all the desktop reverts anyway to the default look Widgets etc configuration is in the file: /home/"yourusername"/.config/*appletsrc file and user icons probably as /home/"yourusername"/.local/share/applications/*.desktop files.
Problem 2 - I have learned that it is better not to mess with desktop widgets icons etc. So I have just that Phone and Phonebook icons and that's all. From time to time all the desktop reverts anyway to the default look Widgets etc configuration is in the file: /home/"yourusername"/.config/*appletsrc file and user icons probably as /home/"yourusername"/.local/share/applications/*.desktop files.