Magnetic flux induced in toroidal core and conductor position
The magnetic core has low reluctance. Low reluctance means that it is a very attractive path for magnetic fields to flow through compared to air hence, most of the circulating flux in the toroid will be constant largely irrespective of the conductor position. This is because the magnetic field strength is dictated by current flow and it is assumed, for this explanation, that current flow is constant.

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 extremely long and reluctance increases linearly with the circumference. 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.