I've tested this tip with Ubuntu 20.04.1 LTS.

Remove unwanted desktop icons

You can use a tool called Tweaks to remove Home and Trash from the desktop.

First, install Tweaks:

$ sudo apt install gnome-tweaks

Next, launch Tweaks and navigate to Extensions. Click the gear icon within Desktop icons. Then turn off personal folder and trash:

Add "Show Desktop in Files" to the dock

When you right-click the desktop, there is a function called "Show Desktop in Files". You can add a similar function to the dock.

First, create a new application:

$ sudo nano /usr/share/applications/show-desktop-in-files.desktop

With the following contents:

[Desktop Entry]
Type=Application
Encoding=UTF-8
Name=Show Desktop in Files
Exec=sh -c "nautilus --new-window ~/Desktop"
Icon=user-desktop
Terminal=false

The application you created is called "Show Desktop in Files".

Next, find "Show Desktop in Files" in Applications. Then right-click and choose Add to Favorites:

"Show Desktop in Files" is available in the dock:

Put downloads on the desktop

By default, downloaded files are stored in ~/Downloads. You can use the desktop instead.

To use the desktop to store downloaded files:

$ rmdir ~/Downloads
$ ln -s ~/Desktop ~/Downloads

You can do a similar thing for other default directories, including ~/Documents and ~/Pictures.

Dave's Notes