As for re-materializing matter that hasn't completed going through, I think that was an issue in the episode of SG-1 where Teal'c got 'stuck' inside the gate. But it was so long ago I can't remember.
They accounted for the icing effect the same way they reasoned that the Stargate was only able to dial to Abydos at first, stellar drift or whatever. They would get iced because it was a 'bumpy ride'.
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