Heh. In my book, no question is unnecessary, if you don’t know the answers.
So, your original connection (the TV part) is correct. The Beam goes to the ARC port on the Frame’s connection box, the Apple TV goes to any other HDMI port on that box.
If you’re using the Amp to drive a set of surround speakers, then yes, it would connect wirelessly to the Beam. Sonos engineers apparently call it via SonosNet, but I object to that appellation. In any case, it’s a ‘hidden’ 5Ghz connection, and it’s called ‘bonding’, which places both the Beam and the Amp in the same Sonos ‘room’, so they’ll play at the same time when using the TV input.
That being said, you could also choose to set up the Amp separately, in which case it connects to your router, either via Ethernet, or your WiFi signal. You could then group the two ‘rooms’, and play streamed music in sync, but the Beam’s TV input would be delayed on the Amp’s ‘room’.
It depends on what you want. My recommendation is the former, but there’s nothing wrong with the latter, either.