Learn Turkish: Matbaayı icat eden adam çok yaşlı. - The man who invented the printing press is very old.

Because it is the direct object of the verb icat etmek (to invent). Even though icat eden acts like an adjective describing the man, it still takes objects just like a regular verb. Because the printing press is a specific object being invented, it gets the accusative suffix -ı (with a y buffer).

This lesson is about the passive suffix -Il. How would we use it with this verb?

This specific sentence is in the active voice, using icat eden (who invented). To make it passive, you add the -il suffix to the helper verb etmek. The t changes to d, making edilmek (to be invented). For example, if you wanted to talk about the printing press that was invented, you would use the passive participle and say icat edilen matbaa.

Why does etmek change to eden instead of eten?

This is an example of consonant mutation. When the helper verb etmek takes a suffix starting with a vowel, like the subject participle suffix -en, the t softens to a d.

Could we use eski instead of yaşlı for old here?