Is this normal: the direct Ethernet is 5x faster than the same Ethernet via Airport Express

what you want to do is setup your express to be a "bridge" for your airport extreme network, you want to create a "new" wireless network (but if you use the same settings as your extreme, most macs should seamlessly work and switch as required)

make sure your airport express is configured not to do any NAT or give out IP's as that is maybe what is conflicting with your network currently, also make sure you give it an IP in the same subnet as your airport extreme and also that it does not conflict with any other machines

Check what wireless networks are available. It is possible your Airport Express is broadcasting a secondary wifi network. If so, try connecting to that network and searching for base stations again.

As a last resort, you can perform a reset. Try a configuration reset first (hold the reset button down with the tip of a pencil for a few seconds, until the led flashes rapidly). If that doesn't work, try a factory reset, by unplugging and replugging it, holding down the reset button.