Learn Hardcore Turkish: Her bağımsız bölüm için ortak gider ödenecek. - A shared expense will be paid for each independent unit.

Literally, bağımsız bölüm means independent section/unit, but in Turkish property and apartment-building language it is a fixed term. It usually refers to an individual legal unit in a building, such as:

an apartment
an office
a shop

So in this sentence, it is better understood as each individual unit rather than a general section.

Why is it her bağımsız bölüm and not her bağımsız bölümler?

After her meaning each/every, Turkish normally uses the noun in the singular form.

So:

her bölüm = each section/unit
not her bölümler

This is different from English, where learners sometimes expect a plural idea because the meaning is distributive. In Turkish, her + singular noun is the normal pattern.

What does için mean here, and why does it come after the noun?