Does gold collected affect the damage of hireling with adventurer set? (When player character has/has not wear Adventurer set)
Does Crystalline and eternalized set on hireling affect the drop?
It doesn’t affect your drop. Only what your Main Character has equipped is affecting the drop.
I’m speaking of Set Affixes. But keep in mind that both you and your hireling should have roughly the same% of Gold Find and Item Quantity and Luck, since these affixes are affecting your drop when playing with a hireling.