So if the library consists of various locations, and you arrange your files by, say, author, and you drag a bunch of files in there from he desktop like David is doing at 9:00 in the video... in which of the locations do they actually end up? I suppose it just moves them to whatever location was set as the default save location.
Correct. Each library has a default save location that you can modify at will.
Also: will the federated search work with Windows Home Server?
Yes.
What if I'm not at home, but I want to play an mp3 that's on my WHS music share. Can I just use any music player's common file dialog, and open that file remotely through federated search? Although I suppose that all depends on wether the WHS team releases a search connector for WHS shares, right?
Libraries do not allow remote locations, so this scenario is not supported. The main reasons are relevancy calculations (that may differ completely between sources) and network latency (that would drastically impact aggregated views).