ARRISSurfboard mAX W122 Mesh Wi-Fi 6 System | AX6600 Wi-Fi Speeds up to 6.6 Gbps | Coverage 5,500 sq ft | 4.8 Gbps Backhaul |Wall-Plug Satellite | Two 1 Gbps Ports | Alexa Support | 2 Yr Warranty

Q: Can i use this router to extend the range of my arris surfboard sbg7580ac cable modem router? (connect from existing to this one via ethernet cable)

you could but why not use a wifi extender for 30 or 40 dollars? NETGEAR Wi-Fi Range Extender EX6120 - Coverage Up to 1500 Sq Ft and 25 Devices with AC1200 Dual Band Wireless Signal Booster & Repeater (Up to 1200Mbps Speed), and Compact Wall Plug Design

Q: Is this compatible Wave broadband?

Itself is Wave broadband. I use two to cover my house plus my old wireless modem for the extended range. But I don't think it will wave with other wave devices if "compatible" means co-exist with other brand.