I don't know of anything that could make this work, unless some new capability has been added to the latest official firmware 1.03.06 or 1.03.11.
That's easy, any DLNA media player will do that (with the right codecs and enough power).There are a number of other apps on the play store including one that plays media from the humax on a phone/tablet
Not with a HDR-FOX as the data source. Sky Go subscribers get their live TV on-the-go as an Internet stream, anyone else can do similar using the CatchupTV app or web site....and an interesting one that seems to allow live streaming of TV
Again, not possible on an (unmodified) HDR-FOX, unless there are hidden facilities we know nothing about....and remote recording.
Just tested it on two Fox T2s.I've knocked up a package which, at least on my box, lets the Humax Remote App function - it's called rc-app-bridge
I'm not sure there's any real point to it but it was an interesting exercise!