I'm not familiar with the software setup or control of the CAV6.6. That may be worth digging into as that would be the central control point for the whole house audio (WHA). All of your sources need to connect to the CAV and then it will handle sending them to the proper rooms and adjusting volume as you choose. That's typically what a keypad in the room will do, or with a more advanced system, it is what a phone interface can allow for.
Yes, you need to make analog (red/white RCA jacks) connections to the CAV. This is life these days, and so the cable tv tuner, needs to push out both HDMI audio as well as analog audio on RCA jacks. You run into issues when you start mixing HDMI only devices with distributed audio when you have both surround sound areas (living room) and stereo areas (everywhere else) because HDMI doesn't support both stereo and surround sound at the same time. This means you have to force all of your HDMI only devices to stereo only if you want to hear them in rooms outside the living room.
If you contact your cable TV provider, they may offer cable tuners with legacy connections on them. That may be worth having if you want TV audio everywhere.
I expect most decent CD players to have analog audio connections on it, so that shouldn't be a problem.
Same with many Bluetooth receivers. Maybe consider something better than Bluetooth like Sonos or similar for audio playback with a modern phone interface.
The job of the CAV is to allow any room to select a source and then adjust volume up and down for that source, or to turn that room's power off so no audio is playing in that space.
The job of the amplifier is to just amplify audio to the pair of speakers (or 4 speakers) in that room. A good amplifier will be at least 4-ohm stable so it can handle a couple of pairs of 8-ohm speakers in it. This is common usage.
What concerns me most is that I'm not sure how you control the CAV from the extra rooms you have listed that don't appear to have a wall-controller in them.
I'm just not familiar enough with the Russound ecosystem and their constant discontinuance of products to have a clue how you would control all those separate rooms. I lean towards using the Crestron BIPAD8 with a CP2e processor instead. In my world this can give someone up to 8 sources to up to 8 rooms with an interface which works on the iPhone. Basic, but works well.
I found some decent photos of the CAV here:
https://www.amazon.com/Russound-CAV6-6-Controller-Discontinued-Manufacturer/dp/B0006V7308