1) This one depends on context, but most likely it means that she beat you badly. "Put you under" likely refers to the burial of a dead body; if you lose badly to someone, it's likened to death.
2) "go over well" refers to how a certain event played out or will play out. If something goes over well, the outcome was good. So, if you had a good job interview, you could say, "My job interview went over well today." On the other side, if you bought a different kind of coffee at Dunkin Donuts, like the example, and it tasted bad, you could say, "it didn't go over well."
3) The commentators were talking about race statistics and things that didn't relate directly to the events of the track. Most likely the video footage was also just of the people talking. When they say "kick it down to the track", they are transitioning to talking about the actual race. The video footage will change to footage of the racers instead of the commentators. "Kick it down" is just said to express that they are kicking (moving) it (the subject of conversation) down (since they are in a booth) to the track.
4) I have no idea what this means without context.