Network traffic goes via WiFi or Ethernet. The connection to the TV is via HDMI. HDMI will have HDCP - aka High Definition Content Protection. However the TV will have to decode the signal as otherwise it couldn't display anything on the screen for you to watch. At that moment they can see exactly what you are seeing. It doesn't require the data/internet stream when they have the image (and sound) stream itself. You can easily fingerprint content based on that.
No, but they don't need that. And HDMI isn't open either as it has content protection. But ultimately you want to watch something so that chain is broken and guess what, it is the TV doing that, that is its core job. So it can 'see' at all times what you are watching.
Now whether they actually do something with that data beside automatically adjusting the picture quality, or ambilight (Philips does that), or phone home to keep a database of all the programs you watch. That is a whole different matter, they can, but are they really? Nah...Eitherway, having your source on the VPN isn't going to stop that.