Nest Wifi - Mesh Router (AC2200) and 2 points with Google Assistant - 3 pack - Snow

Yes, AC2200 is Nest WiFi router while the AC1200 is Nest WiFi point. You can connect them to each other wirelessly to create a mesh network.

Arris Surfboard SBG6700-AC is a modem/router combo. You won't need to purchase a separate modem for Nest Wifi system to work with it. But, when you connect Nest Wifi router to your modem/router combo, you will technically have two routers, each broadcasting its own private Wi-Fi network. This situation is called a Double NAT and may lead to some problems depending on your use of Wi-Fi. You can either put your modem/router combo in Bridge mode or disable the Wi-Fi functionality of your combo to avoid Double NAT. Here is a link for you to find out more about Bridge mode and Double NAT : https://support.google.com/googlenest/answer/6240987?hl=en If you prefer to disable your combo's Wi-Fi functionality, you can reach out to your internet service provider (ISP).

Nest Wifi isn't compatible with 3rd party routers like your Centurylink modem/router combo to form a Wi-Fi mesh network. You can only combine Nest Wifi and Google Wifi to create a Wi-Fi mesh. A good workaround is to set up your CenturyLink combo in bridge mode and disable its Wi-Fi functionality. You can then connect Nest Wifi Router to your combo using an Ethernet cable and connect your Nest Wifi Points to it.

Yes, I have over 5000 sq ft, 3 level home. The router is located on the upper third level floor, one point on the first and second level ; The 1st level floor is 12 ft cement block walls and wifi is great on all three levels.

No — the points no longer have an Ethernet option like the legacy product had.