Does the presence of grease, oil, or ink on the parts of the body designated for ablution (wudu') prevent it, as well as earwax and dried eye discharge? Are there authentic hadiths to that effect, and have scholars agreed on their ruling?

The rule is that anything preventing water from reaching a limb invalidates ablution (wudu'), and anything that does not prevent water from reaching a limb does not invalidate ablution. Thus, ablution is valid with ink. As for grease (or ghee), if it has a solidified body that prevents water from reaching [the skin], then ablution is not valid. But if it is a trace or a liquid, then it is valid with rubbing. Frozen eye secretions must be removed according to some scholars. As for earwax, what is on the external ear canal should be removed, but not what is inside the ear.