with an Android TV could I install VLC on that and watch programmes from the HDR directly over Ethernet?
I don't think it has to be specifically an Android TV, typically "smart" TVs have a streaming client (although early ones were a bit limited with format compatibility - M2TS masquerading as TS is a stumbling block). The point about VLC is its ability to handle that kind of thing, and codec switching mid-stream (as happens in broadcast data).
Choosing a TV implementation of Android should result in having an app store available, but the actual content of that store will depend on the manufacturer having chosen to make any particular app available - they all need vetting and possibly tweaking, or at the very least the manufacturer wants to retain some control. Same applies when it comes to Android updates - the various phone makers release updates for their phones a considerable time after Google has released an Android update (if at all). Basically, check for VLC app availability for that specific model of TV before you buy.
The HDR-FOX authenticates a DLNA client by DTCP, which is a cryptographic handshake intended to verify that a streaming client does not have the capability of saving the streamed content. If DTCP fails, the HDR-FOX refuses to stream protected content (ie HiDef recordings, unless you've unprotected them by running the
unprotect package). We know the HDR-FOX accepts other Humax PVRs as secure clients, maybe including the Aura, and perhaps it will accept TVs... unknown. Not a problem if you unprotect of course.
However, the playback by DLNA isn't as "nice" as playback natively, and personally I would prefer to use an HDR-FOX (or even HD-FOX using file sharing) than DLNA from VLC... although if you're going for a cable-free installation that isn't going to work for you.