can anyone tell me whether both ports on the new Airport Express are available (as LAN ports) when it's extending an existing AEBS network? (I have read conflicting opinion.)
Both Ethernet ports act as LAN ports when the "new" Express is configured to "Extend a wireless network" using a wireless only connection. This is not an opinion, it is a fact. The same is true regarding the 4 Ethernet ports on an AirPort Extreme configured to "extend".
I assume that a small switch needs a power supply (?)
Is there such a thing as a standalone unpowered (or long-lasting battery) version available?
Passive hubs do exist, but I doubt that the AirPort would provide enough power for the device, since it does not offer a PoE (Power over Ethernet) feature. Have not seen a battery powered hub.
Yes - both ports are LAN ports in this configuration - and all fast ethernet switches need power - they come with an AC power adapter - I couldn't find any that are battery powered but here is a link for one that works off a powered USB cable -
There are POE ethernet switches available but they are very expensive and would require a POE injector because the ports on the Express are not powered.