Those clips of the Subaru are a good example of the kind of fluid motion you’re going for. Leo’s examples (unicyclist.org) lack the fluidity but otherwise show the motion. When a beginner does it, it looks like a 3-point turn in a car. But the Japanese girl shows what it’s supposed to look like.
There isn’t an official name for the frontspin/backspin hop thing, but I call it an axle jump. Hers is a little one, but I believe that’s what she was trying to do. If you work at it, it’s possible to get a full 360 in the air (but not easy).
I don’t know exactly who she is, but there are a lot more where she came from; Japan. When they get together for their big Freestyle competition there, they call it Unicycle Dancing.