Some of these come pre-assigned (email, mute, volume- & volume+) The others (HomePage, Search, 1-5, & Calculator) have to be manually assigned. Also, so far I have not been able to assign Search & Calculator.
Step 1: Creating the custom command.
Open System Settings -> Keyboard -> Shortcuts
If the action you want is not already listed under any of the menu options create a 'Custom' shortcut at the bottom by selecting 'Custom' then pressing the '+' to create a new entry
type the command you want (e.g. "io.elementary.calculator %U" to open the calculator)
after typing the command click on the right hand side of the row (where it says 'Disabled'. This will prompt you with 'New Accelerator...'
Press Shift & the button you want to assign (e.g. media key 1). This will show you "Shift + " then the name of the key (e.g. "Shift + Launcher5" for media key 1)
Continue adding your custom shortcuts this way.
What's that you say? You don't WANT to have to press Shift each time? Well move on to the janky part...
Step 2: Editing your dconf (yikes)
Install dconf editor from the AppCenter. Open it
You will see a folder structure open up: org > gnome > settings-daemon > plugins > media-keys > custom-keybindings (there is a folder and a key.. you want the folder up top)
Here you should see custome0, custom1, etc. Open the one you want to edit.
Click the 'binding' key to edit.
Lets say you used Shift + Launcher5 as in our example. Edit the 'Custom value' text (you'll first need to toggle off 'Use default value') and remove the '' from the text.
Press the 'Apply' button at the bottom of the dconf editor.
Test!