Remove trash icon from GNOME desktop and add to Ubuntu dock

I just installed Ubuntu 18.04 and don't like having the trash icon on the desktop rather that in the launcher (Ubuntu dock).

How can I move it back to the launcher? Can other icons be moved from the desktop to the launcher?

Removing the Trash icon from desktop

Up to Ubuntu 18.10

Launch Terminal and run

gsettings set org.gnome.nautilus.desktop trash-icon-visible false

You may alternatively use GUI tools like dconf-Editor or (GNOME) Tweaks (see this for reference).

Ubuntu 19.04 and later

Disable the trash icon option from Extensions > Desktop Icon in Tweaks:
Alternatively, run the following command

gsettings set org.gnome.shell.extensions.desktop-icons show-trash false

Adding a Trash icon to the Ubuntu dock

Up to Ubuntu 19.04

Follow the steps below.

1. First install the trash-cli package by running

   sudo apt install trash-cli
   

2. Create a .desktop file (say trash-in-dock.desktop) in your ~/.local/share/applications/ directory.

3. Open the file with a text editor and add the following lines

   [Desktop Entry]
   Comment=Trash icon for Ubuntu dock
   Terminal=false
   Name=Trash for Dock
   Exec=nautilus trash:///
   Type=Application
   Icon=user-trash
   NoDisplay=false
   Actions=empty-trash;
   
   [Desktop Action empty-trash]
   Name=Empty Trash
   Exec=trash-empty
   

4. Save the file and re-login if needed.

5. Click "Activities" or press Super and search for Trash for Dock. It should appear in the results.

6. Right click the icon and select "Add to Favourites".

What you will get

1. A Trash icon in your dock, clicking which will open the Trash folder.

2. Right clicking the Trash icon in the dock will show an "Empty Trash" option which should work as intended.
   

What you won't get

1. The Trash icon in the dock would be like other app icons, it won't be conveniently placed at the bottom like in Unity Launcher.

2. The Trash icon in the dock would be a 'static' one, i.e. won't show two different icons depending on whether the Trash is empty or not.

Ubuntu 19.10 and later

Simply run the following command

gsettings set org.gnome.shell.extensions.dash-to-dock show-trash true