Learn Turkish: Bir kültürü özümsemek zaman alır. - Internalizing a culture takes time.

The root is öz, meaning "essence," "self," or "core." The suffix -(ü)mse-mek is used to derive verbs that express an attitude, perception, or feeling toward the root word. So, özümsemek literally means "to treat something as your own essence," which naturally translates to internalizing, assimilating, or absorbing it.

Why is it bir kültürü (with the accusative -ü) instead of just bir kültür, since it translates to the indefinite "a culture"?

The verb özümsemek strongly prefers a specific object because you are actively focusing your mental attitude on it. Even though bir (a/an) is used, adding the accusative -ü makes it a "specific but unnamed" culture—as in, "a particular culture you are trying to internalize." Without the accusative, bir kültür would sound too generic and detached for a verb of deep personal perception.

Is zaman alır a fixed expression, and why is it in the aorist tense?

Yes, zaman almak is the direct equivalent of the English idiom "to take time." It is written here in the aorist (broad) tense (alır) because the sentence is stating a general, timeless fact about human behavior, which is the primary use of the aorist tense.

How does the sentence structure work here with two verbs (özümsemek and alır)?