The power adapter is what plugs into the router to a power source that turns on the router. The cable I believe your referring to is the uplink cable / ethernet cable fom the modem port to router uplink port.
It should work fine, my paperwhite has no issue. Keep in mind the wifi on this router has 2 bands, one at 2.5 and the other at 5 GHz. My paperwhite (and many computers) can only 'see' the 2.5 GHz signal. Now normally, the default passwords that come with the router are the same for both bands. If somehow the Passwords are different, and your paperwhite is trying to join the 2.5 band, but you are using the PW for the 5 GHz band, you won't be able to sign on. If you have an iOS device and you pull up the wifi connections available, you will see both bands, as the Apple products can connect to either.