Extend Wi-Fi on a non-Apple network by Ethernet with an 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

There shouldn't be any issue with using the Airport as an extender in that scenario.

Normally an Airport can only extend the wireless network by providing a bridge over Wifi between itself and another Airport (or Time Capsule)

Using an Airport as an extender with a non-Apple router requires you to connect the two using ethernet, usually with a physical cable however by using a powerline connection that will replace the physical cable with the Ethernet over powerline.

A few caveats, if you are using MAC address filtering on the ethernet interface of the devices, make sure you add the MAC addresses of the Powerline module connected to each as required. Normally most routers only limit MAC address filtering to the Wifi interface, but there are some that will alow you to enable this on all interfaces.

Edit: There shoudn't be any issue with using the AirTunes functionality under this scenario either as well as it providing the required Wifi extension.