It found the DLNA server on my router, so should find your Airport if it's running its server. Getting the WiFi going was relatively painless, especially with a USB keyboard connected to enter my secure key. Note you cannot use the WiFi and wired connections at the same time... not sure if you can host an AP while using the wired ethernet? Manual is pretty thin on smart features, but online help is better.
Yes, I have mine connected to an Apple Airport Extreme. The only problem I have encountered is that the Samsung allshare is not Mac friendly. I had to find and use an alternate media server in order to view my movies.