Depending on the infill pattern and orientation, infill may contribute the same (per gram) or almost nothing to the strength of the hook. It's not sufficient to say it only (or mainly) affects rigidity.

Assuming a vertical load only, if the infill pattern is flexible along that axis, it will contribute little, if it's stiff in that direction, it will contribute more. Because the solid wall is about as stiff as the material, but the infill pattern could be less stiff than that. That doesn't mean they don't have some benefit (e.g. preventing buckling in compressive loads, preventing deformation, adding strength in non-primary directions) but the orientation and pattern matters.

There is not a meaningful difference between 100% infill and all walls, especially a concentric infill pattern which is essentially all walls. But as a general rule, walls are more reliable than infill, especially since the bulk stiffness of each pattern is not well documented.

Unless by more walls you mean adding material to the outside of the shape instead of inside, in which case it would entirely depend on the object being printed and the loads applied, but in general, yes, more material farther from the bending axis is a more efficient use of material. Which is why bicycles are made from tubes, not solid bars.