AirPlay doesn't work when AirPort Exp. extends my network?

It will work wirelessly if you are able to get Wifi from some of the old routers. In other words: you need Wifi signal from your existing network for both your AirPort Express and the Apple device to use AirPlay in this configuration.

The Airport Express will work on client mode and will not extend your network, but it will allow AirPlay. This is because AirPorts do not wirelessly extend non Apple networks. See this question for reference.

I have a similar setup in my home, and my solution was to run an Ethernet cable to the AExp to be able to use it to extend my network, and do AirPlay.

On the Error -6753, I've found someone suggesting you have to enable IPv6 on your router.