How do I connect Airport Extremes & Expresses to a hardline Ethernet?

Each is set to "Extend Existing Network" (or whatever the exact phrase is).

Wrong setting. "Extend a wireless network" is used only when the AirPort connects to another AirPort network using a wireless connection.......not Ethernet. As it stands now, you are creating big feedback loops for each Express network, which effectively crashes the network in the area near each AirPort Express.

The correct setting would be "Create a wireless network" using the same wireless network name and password of the wireless network that you want to extend. And.....check to make sure that each AirPort Express is set up in Bridge Mode, which Apple calls "Off (Bridge Mode)".

If you are still having trouble, post back and we'll start all over with each AirPort and set it up the correct way using the AirPort Utility setup "wizard", which will automatically apply the correct settings.

The trick here.......you must connect the Express to Ethernet......before.....you run the setup utility, so the "wizard" will pick up the Ethernet connection and apply the correct settings.

If you don't connect the Express to Ethernet before you set it up, the "wizard" will pick up the wireless connection and configure the Express to connect using wireless. Then, when you connect Ethernet, a huge feedback loop is created, crashing that portion of the network.

Unfortunately, Apple never bothers to mention things like this in the Setup Guide.

Reset the airport to factory before you plug it in.. They are likely setup wrongly and will crash the network without a reset before configuration.

Once you have reset plug wan airport to the switch.. and open the airport utility.. click the Other WiFi Devices (1) on the main screen and simply run through the setup wizard..

Use short names, no spaces and pure alphanumerics for everything.

Password same rules but longer.

It should work .. if it fails give us screenshots from the Airport utility with the setup so we can see what is failing.

Nice work!

Not to be too technical here, but what you have is known as a "roaming network". That is a form of extended network in which all of the AirPorts connect using Ethernet and all of them are configured the same.......to create a wireless network that uses the same wireless network name, security and password.

There is virtually no limit to the number of AirPorts that can be configured in this type of network, so additional AirPorts can be added as needed providing there is an Ethernet connection available at the location.