Regarding point 2, the article gave me the impression that they used historical measurements of the the mains frequency as part of the analysis. Since Britain is on a single grid, the local conditions shouldn't affect the recorded signal. I'm sure it is possible to find patterns (frequency drops slightly in the morning as the public utility tries to keep up with increasing demand), but you wouldn't know, for example that the utility overestimated demand on the particular morning that the audio was alleged to have been recorded (and thus that the frequency was actually higher).

As for point 1, there are a number of plausible angles to approach this, but I think that the forensic adversary has a huge advantage: Synchronous detection. The approximate time of the recording is known, as is the historical record of mains frequency. That allows for the possibility of huge processing gain, which might allow for recovery even after the amplitude of the mains hum is filtered to below the quanta of the audio system. I almost think you might have to Fourier Transform the whole audio record and zero out any component at f_mains +/- delta (and harmonics). That, of course, would look pretty suspicious to a forensic analyst.

Even that might not be enough if mains hum has a determinable effect on the data compression algorithm used to store the audio data.

Edit: The point I was trying to make in the first paragraph is that if you wanted to forge a recording, you'd need to have the grid frequency data. Having it for anywhere would be good enough and not having it for anywhere simply wouldn't.