How does she achieve recording of clips without any latency?
Low latency soundcard. Nothing special.
Why doesn’t she use her Octatrack?
She has set a small buffer size in her Ableton Live settings. Since she is on a Mac, this can be done with the default CoreAudio drivers. On Windows, using ASIO drivers is essential. Depending on your system performance, you can go very far, and even below 5 ms of latency.
Did anyone notice, that when the video shows her screen in full size, her Ableton Live has a different visual theme (darker) than when they show it from distance (brighter)? 
What happened here? 
It’s the same theme. When it’s shown full-screen you’re looking at a screen recording done directly on the computer and not through a camera.
It just looks brighter in the camera shots.
Whoever edited the video could have done a better job matching colors, maybe.