Learn Turkish: Uzun süre kimyasallarla çalıştığı için, akciğerleri hasar gördü. - Because he worked with chemicals for a long time, his lungs got damaged.

You would need to change the cause into a verbal noun and the effect into an object taking the dative case. It would be: Uzun süre kimyasallarla çalışması, akciğerlerinin hasar görmesine sebep oldu. (His working with chemicals caused his lungs to get damaged.)

Why does için take the -DIğI suffix in çalıştığı instead of the -mA verbal noun we use with sebep olmak?

When linking a factual, completed, or ongoing action to için (because), Turkish requires the factive participle -DIK (or -(y)AcAK for future). Think of it as "because of the fact that he worked." In contrast, sebep olmak requires a standard verbal noun (-mA) to represent the action itself as a noun: "caused his working."

Why use gördü (saw) in hasar gördü rather than a passive verb for "got damaged"?

While you could technically use a passive verb like hasarlandı, it is much more natural and common in Turkish to use görmek (to see) with certain nouns to express undergoing a process or receiving an effect. Hasar görmek is the standard idiom for "to get damaged", just as zarar görmek means "to get harmed."

Does uzun süre (for a long time) need a postposition like (throughout/for) after it?