it almost certainly still has an externally accessible ip at that point for management purposes. (bridge 2 interfaces, add a virtual interface to the bridge)
Management for the DOCSIS modems is definitely done over IP. It isnt over SSH but via a webapp controller. This webapp is used to push the firmwares which have the speed limits set in them.
Yes, but by default a modem from your ISP is acting as a NAT device routing to a private IP space. By default, it has an externally available IP address and will answer on that or those addresses.
Many can, however, be configured as a bridge, which turns the device into just a converter between physical mediums. You now need another device to route and act as your gateway. In that setup you shouldn't be able to find it with an IP connection scan, because it doesn't have one.
> Yes, but by default a modem from your ISP is acting as a NAT device routing to a private IP space.
Not in my experience. The default modem provided by both Comcast and Knology (who is -I guess- now WOW!) is (or was, in the case of Knology) a bridge device that requires you to provide your own router. You have to ask for a modem that's also a router to get something that's not a bridge.
That doesn't mean that the modem doesn't have an IP address, mind. AIUI, on Comcast's network the modem gets an IPv6 address so that they can do network management stuff to it.