I'd somewhat agree that xGF and HDCF are the 'most important' but as with everything there's nuance. You're can't ignore other parts of the dataset to build a model that suits a specific narrative. In this case, the narrative is 'they dominated the metrics battle' which isn't true. Even if you wanted to say they dominated the xG/HDCF battle, that's not even true. They won it, sure.
Not exactly, xGF is total amount of expected goals based on fenwick attempts. It has some issues, because if you take 80 fenwick attempts, but they're all from the point, you're still going to generate a reasonably high xGF. But' you'll also generate a high xG if you only take 10 shots from high danger shots. I think a better option for shot quality is 'shot danger' --basically fenwick attempts divided by the xG. Then on average, you can see how dangerous each shot was as described by that specific xG model.
HDCF is a specific metric to NST. And it's somewhat ambiguous for a host of reasons. Basically each corsi is given a value between 0-3+. Any shot with a 2+ rating or higher is a scoring chance (SCF/SCA), and any corsi with a 3 or higher is a HDCF. There are some drawbacks with this, it misses some nuance IMO, but it's a good 'back of napkin' type analysis.
You've right, CF is a proxy for possession and zone time. You can't take lots of shots without having the puck in the offensive zone for a long time.
xG does not use CF numbers to generate the value, only Fenwick numbers, because as I said above, the RTSS dataset does not provide shot location values for blocked shots, only a location value for where the block occurred.