Recordings are stored on your V6's hards drive and won't be affected by loss of Internet, however the "rogue" recordings may be OnDemand bookmarks rather than genuine recordings.
With that in mind, all the functions you're having problems with are internet-based, your V6 connects via your home-hub. Is it connected by Ethernet cable or is it WiFi?
If you follow Home > Help & Settings > Settings > Network, what is shown in the top-right?
Finally do you get any error codes when VoD fails? You should do, and that will help ID what's going on.
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