The Amp will connect to your TV by HDMI-ARC, which is a slightly different connection than regular HDMI.    Your TV needs to have an HDMI-ARC port in order to use it, or an optical output to use with the Sonos adapter.  There’s more to it than that, and it’s worth looking into deeper before making a purchase, but essentially, the answer is yes.

The amp is designed to power a stereo pair of speakers.  You can connect 2 pairs of speakers to the amp (if they are standard 8 ohm speakers), but you still would be getting stereo.  You can ‘bond’ it with a second amp, or other Sonos speakers,  to give you the rear surround channels.  Because you already have the speakers in place wired to a front location, it may make more sense to use a traditional AV receiver instead of the Sonos amp.  You can still include that amp into a Sonos network by using a Sonos Port with your receiver.

That said though, the placement of the speakers is important. The front channels in a surround system should be coming from the front wall, not the ceiling ideally.  Likewise, rear channels should be coming from behind you, preferably at seating level.  If your speakers are more centrally located in the room, it’s not going to sound right regardless of the amp you use.  You may want to ignore them or just use them for music only, a separate system for TV audio.

The Beam is a soundbar that will cover your front channels in home cinema, and of course play music too.  In terms of using it in conjunction with an amp, it can be bonded with an amp where the amp is playing rear channels.  Of course, you can also use Sonos speakers for rear channels, where an amp powers the ceiling speakers only for music...or just ignore the ceiling speakers.

Per your last question, the Sonos system is very expandable, and yes you’ll need additional equipment when you add rooms.  Essentially, each Sonos device is capable of being it’s own room, playing it’s own or audio or ‘grouping’ with other rooms in your Sonos house. Also, certain devices can be ‘bonded’ with other devices to form a single room.  Example of bonding would be home cinema setups like we already talked about, a stereo pair of speakers, or adding a sub to any room.

The best course of action might be to start off with a Sonos Move.  It won’t work with your TV, but you can easily move it around to see how you like Sonos in different rooms, including outside.  And it’s the only speaker that also has bluetooth, so you can use it away from home as well.

I have a semi similar set up, I would recommend what I have if you have the budget for it. Beam and 2 Amps.

Instead of using the HDMI for the sonos amp get a beam, that even comes with an adapter from optical to HDMI if your TV has no ARC. That will cover you for center, left front, right front.

If you add a single amp you can connect it to a speaker switch, this means the rear speakers (behind a couch) could be selected when using it as a left rear and right rear, then when wanting more sound for music or parties you can select both sets and have the whole room filled nicely. 

If you had 2 amps you would gain the ability to select the speaker pairs individually. Or add more speaker pairs. You can even add a non sonos subwoofer to the mix right from the amp. However from my experience the sub cannot be added to the tv for a "5.1" it would only be for playing music.

For expansion just keep adding amps or play devices. It would scale very well for adding zones.