The magnetic core has low reluctance. Low reluctance means that it is a very nice path for magnetic fields to flow down compared to air hence, most of the circulating flux in the toroid will be constant largely irrespective of the conductor position.
There will be some flux in the air but, for a high permeability core (low reluctance) it will be a small percentage.
If you made the toroid extremely large, the path the magnetism travels along gets longer and reluctance increases linearly. If you continued this train of thought, you will get to a point where air carries the most flux because it is seen by the flux as being the preferred path due to it having lower reluctance than the massively oversized and distant toroid core.
See my answer here for a mathematical explanation of how reluctance works in a similar type of problem.
If N parallel strands carried N amps, this is the same as N looped strands carrying 1 amp. Parallel strands are counted as one loop.