I think you've been seeing too many good transformers. The cheap s**te coming in from China nowadays has most loss due to saturation of the core - your (ii) and (iii) above. Worse still it varies wildly from batch to batch.
Not really, because the iron losses will flatten out as you reach saturation. When the core is being driven into saturation the main source of increased loss is copper loss in the primary, due to the magnetising current shooting up.
Find yourself a better manufacturer. Nor everything cheap from China is crap.
That assumes a linear saturation across the iron, which doesn't appear to be happening. It generates large numbers of harmonics (up to 11th at high level) which is unusual and I think the iron itself is displaying some form of hysteresis that varies across itself, and this is actually causing heating in itself. But I agree this is difficult to prove either way.
That's what I advised my client. But have built a rig to quickly test goods in for really bad ones.
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