I would say that 'as' meant 'while', or 'at the same time as', in your sentence:
'Shadows crept across the room; and while they crept across, the bright fire made them jump from side to side.'
'Cast from old furniture' does indeed modify 'shadows': it tells you what caused the shadows. (It also makes the picture more detailed, by telling you that there is old furniture in the room.)
The phrase is remote from the noun as a stylistic choice. By defining the cause of the shadows later in the sentence, the writer allows the reader to concentrate on the fact that there are shadows, and that they are creeping across the room.
If the writer put the cause of the shadows directly after the shadows, we would be thinking about the furniture instead.
I hope this helps.
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