You don’t need it connected to the phone line for remote record the activation signal comes via the Sat dish,you only need the phone wire connected for interactive stuff such as ordering box office movies or checking your Sky account via your sky box.
Regards the anytime plus,if you don’t want to use power line adaptors or a very long Ethernet cable,then you need to get yourself a wireless bridge,either the official Sky one (at around£60) or a 3rd party one for less than half that.
It effectively gives your Sky box a wireless Internet connection,most of the wireless bridges need plugging into the mains supply as well,some can be powered by USB but although Sky HD boxes all have USB ports not all Models of the Hd boxes have power going to them.
If its te current smaller 2nd generation model the chances are the USB ports will be dead,1st gen normally do have power going to them.
A easy way to check is plug in the USB lead you get to charge most modern phones ,if it starts charging your good.