You should check their principles one after another for to be completely sure and not self-deluded instead. This is how the science works - by falsification, not doubting. Other than that, the overunity is as well defined as every other energetic efficiency.
Not always - check for example here: Brownian Motion of Graphene: Potential Source of Limitless Energy at Room Temperature
No. Science works by applying lessons learned, like the conservation of energy. This saves us from an endless morass of futile work. This is not doubting, it is just being rational.
The best use you can have for the term "over unity" is to say that it is impossible.
"While the researchers monitored the membranes for only two and three-quarter hours, they expect that this quivering, jumping motion would continue endlessly, allowing nanomachines to be powered continuously."
Extracting energy from the random thermal fluctuations in the speed of the molecules in a fluid will make the fluid colder. It will be a heat engine and such an engine must have he heat source and a heat sink. The sink must be colder than the source. When somebody comes up with a design we may be able to locate the heat sink.
I have seen that voltage peaks of 0.2 V have been observed, no info on the current. What can you drive with 0.2 V? Since these peaks are random you can't connect them in series and they are too small to be rectified.
Perhaps this idea will fall in the same or a similar trap as Maxwell's demon did.