How can I change the color of the marker on the dash that indicates an application is "up"?

in normal GNOME environment

gsettings get org.gnome.shell.extensions.dash-to-dock custom-theme-running-dots-color

will give the present color

Example:

maduri@i7-4770U:~$ gsettings get org.gnome.shell.extensions.dash-to-dock custom-theme-running-dots-color
'#0000FF'
maduri@i7-4770U:~

to set the required color..

gsettings set org.gnome.shell.extensions.dash-to-dock custom-theme-running-dots-color "#0000FF"

for yellow or green color your can replace "#0000FF" with "yellow" or "green".

Alternatively you can use the GUI tool dconf-editor like below

Note: dconf-editor isn't present by default. You can install it from the Software Center.

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You can also make the dot bigger:

For example, to do so run

gsettings list-recursively | grep running-dot

You'll get output like this:

dkb@dkb:~$ gsettings list-recursively | grep running-dot
ca.desrt.dconf-editor.Settings saved-view '/org/gnome/shell/extensions/dash-to-dock/custom-theme-running-dots-border-width'
org.gnome.shell.extensions.dash-to-dock custom-theme-customize-running-dots true
org.gnome.shell.extensions.dash-to-dock custom-theme-running-dots-border-color '#e95420'
org.gnome.shell.extensions.dash-to-dock custom-theme-running-dots-border-width 2
org.gnome.shell.extensions.dash-to-dock custom-theme-running-dots-color '#e95420'
dkb@dkb:~$ 

Then, open dconf-editor as in the image below and make the desired change:

A much simpler way would be to install the Dash to Dock extension and change the marker's color, size and style using the settings it offers.

You can change the Dash to Dock extension settings via Tweaks. If you don't have Tweaks installed, you can install it by running:

sudo apt install gnome-tweaks

After running Tweaks, go to Extensions on the left-side bar and click the cog icon next to the Dash to Dock extension. Navigate to the Appearance tab and you will find the Customize windows counter indicators option, as shown in the following screenshot.

You can select the marker's style using the drop-down menu next to this option (I use Segmented).

To change the marker's color and size, click the cog icon, turn on the Customize indicator style knob and set your preferred marker color and border width. As you can see in the next screenshot, I have chosen a green marker with zero border width (for the purpose of demonstration).