Below the links to the specific sections of that page that address the posted questions:
Frequency filters should be applied on the continuous raw data, rather than on the imported epochs. This is to avoid that the transient of the filter uses a good part of the epoch.
Once source estimation is performed, the data is on the same space, this is to say the Subject anatomy (cortical surface if unconstrained sources are estimated). So it can be averaged without further pre-processing.
If there are multiple runs and the run average is computed for different number of trials (in the run), it is recommended to average the run averages using weighted average, this with the goal that each run has the same weight the in the Subject average.
I have continuous resting-state data of 5 minutes. I noticed that the head distance is not stable over time, so I segment only the periods in which the head was stable, and then I process only those segments separately. I have followed the Brainstorm tutorial step by step for segmenting periods with a stable head. Now, if I apply a notch and band-pass filter on the continuous raw data before segmenting, it can happen that a transient coincides with the first stable segment, and I end up discarding a segment of data. I was wondering if this is correct.