It recommends using ethernet between the Core and Output, but it’s silent about the Core to internet connection. It might be obvious, but it’s probably better to recommend connecting the core to the router via ethernet, not WiFi. This might not be super important if you are playing local files, but might be if you are streaming from Tidal/Qobuz. I’m guessing this guide was written before Tidal/Qobuz was supported by Roon 
I think it depends on your use case. I’ve done it both ways. In the end, I decided to connect my (headless) core directly to my router in a different part of my home and stream to my endpoints, but that was because I didn’t want the (slightly noisy) core in my listening room.
As you suggest, if you aren’t overtaxing your network, then you have more flexibility in your setup. What I would say though is that there are a lot of issues raised due to networking constraints.
They put that in the “networking best practices” section:
under “for all networks” it says: “Your Roon Core should always have a wired connection”
That being said there seems to be some conflicting guidance in there.
Nope. Tidal was integrated on release.