One thing you want to take note is that Apple TV requires Activation like any other iOS device. And that requires a one-time working Internet connection.
You can of course do that with any other's network connection, even with the one in Apple Retail Store.
For the features you request, that's take a look.
Question A. Will it work at all with a PPC Mac?
So the answer is it will. But I am concerned with the version that you have on your PPC Mac. AirTunes (now called AirPlay) has been built in to iTunes for like forever, so that shouldn't concern me. You can use AirPlay to stream at least audio to Apple TV. (Videos are added after iTunes 10 as I believe, but I am not sure if PPC Macs do that)
As I believe, "iTunes Home Sharing" exists on iTunes 10, so if you can run it, and find the option "Home Sharing" under iTunes's "Advanced" menu, you can browse your iTunes library on your Apple TV. BUT, activating Home Sharing, again for the first time requires you to authorize your Mac and Apple TV to use your iTunes account. Again, a one-time thing. (Home Sharing is added before/in iTunes 10, but again, I am not sure if PPC Macs have that)
Question B. Will it mirror my iPhone via AirPlay?
Yes, it will. AirPlay mirroring requires a working LAN connection only, no iTunes account authorization or stuff.
Question C. Will it work at all without Internet?
So, as I have answered the last two question, the answer is obvious, it will.