Does HomePod Mini work on network with Airport Expresses?

It will depend on what exactly you mean by "work with Airport Expresses." Both the AirPort Express base station and the HomePod mini are AirPlay receivers. You can stream, via AIrPlay, to either. For example, if you are streaming from a Mac, both the Mac and the HomePod need to be connected to the same Wi-Fi network ... and that network could be provided by an AirPort Express.

See if the following can help answer your questions:

• HomePod User Guide - Apple Support

Tom Meade1 wrote:

How do you specify a network - this may be an academic question as I have only regular and its 5Ghz equivalent - or are they?…

Does HomePod access the 5Ghz network?

You would typically have one Wi-Fi network with both 2.4 GHz and 5 GHz availability.

HomePod mini can connect to 2.4 GHz and 5 GHz networks.

HomePod mini will pick up its configuration from the iPhone or iPad used to configure it, including the Wi-Fi credentials.

HomePod is a networked device, and one that other network-connected Apple devices will detect and allow as an audio output device.

AirPort Express can be used to create a Wi-Fi network, and as a Wi-Fi-connected audio output device. HomePod mini might be connected to the former (if that’s what you’re using for Wi-Fi), but the latter is largely unrelated to HomePod mini.

Yes, and it comes with a 20W power adapter.

To drive that speaker would require a bit of power that, I'm sure, batteries would not last long.