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No. The pigment is bound within the fiber rather than applied to the surface, so there is nothing loose to transfer. Transfer onto eggs would indicate a surface coated carton with poor adhesion, which is one of the practical reasons we color at the wet end rather than coating afterward.

Slightly, because the pigment loading is higher by mass than for a light tint. That is partly offset by a lower rejection rate, since black does not fail shade checks the way pink and pastels do. Net difference against other stock colors is small.

No, and not because of the color. Fiber texture breaks up continuous tone regardless of substrate, so photographic reproduction fails on pulp generally. A bold single color illustration in white on black reproduces well. A halftone image does not.

Less than any other shade we produce. Black pigment has more lightfastness headroom than light tints, because fading is a proportional loss and there is far more pigment present to lose. Cartons held in strong sun for months will dull toward charcoal, but the effect is slower and less visible than on pastels.

Yes. The pigment is a very small fraction by mass and is selected for compostable packaging use, with no coating or film involved. Buyers sometimes assume heavy pigmentation means heavy additives, but the loading required to reach black in fiber is still minor against the mass of the fiber itself.