Since this is a Sonos forum, I’ll give you the Sonos answer, for answers to 2 and 3, you’ll likely need to look at another forum for non specific manufacturer answers, such as AVS forum or the like. Alternatively, you may want to engage a professional installer, who might give you advice based on what they know, sell and install.

If you read the specs on the Sonos Amp, it can drive up to two pairs of 8 Ohm speakers, or 6 pairs of the Sonance Architectural Series speakers, which are specifically designed for it. Each Amp you would use is its own ‘stream/zone/room’, so you get a single stream and volume out of it. In general, Sonos devices connect wirelessly to your WiFi environment, but the non-portable ones also have Ethernet ports which can be connected (at 10/100 speeds, not gigabit speeds) to your network.

When streaming music to the Sonos system all ‘zones/rooms’ will be synchronized. There will be a slight delay between your home theater setup and any grouped rooms when playing the TV input on your Arc Ultra/Sub4/Era 300s. It won’t make a difference if they’re wired or wirelessly connected. 

Sonos Amps will be the least hassle and give you the ability to play two independent streams in the rooms they are connected to. More Amps if you want more independent streams.

A Sonos Port and external (not Sonos) multichannel amplifier would give you a single stream.

You might consider how you want to control volume if you want different levels in each room.

It seems there are questions not asked of you…

Are the speakers already installed and powered by non-Sonos amp?

If so how many speakers are there…. 8 total or 8 wall and 8 ceiling speakers?

Also how many speakers are driven by a single amp 2 or 4.

Are current rooms stand- alone or adjacent via an open floor concept.