Learn Turkish: Yağmur buna neden oldu.

You are right that neden is the question word for "why"! However, it is also a noun meaning "cause" or "reason". When paired with the helper verb olmak (to be/become/happen), it forms the compound verb neden olmak, which means "to cause".

Why does the word for "this" change to buna instead of staying as bu?

The verb neden olmak requires the thing being caused to take the dative case, which is usually the "to" or "towards" direction. To add the dative ending -a to the pronoun bu (this), we must insert the buffer letter -n-, making it buna. You can think of the literal translation as "The rain became the cause to this."

What does oldu mean on its own here?

On its own, oldu is the past tense of olmak, meaning "became" or "happened". Turkish frequently uses olmak combined with nouns to create new verbs. Here, neden (cause) + oldu (became/happened) work together to mean "caused".

Can I use another word instead of neden?

Yes! A very common synonym is sebep, which also means "cause" or "reason". You can perfectly replace this phrase with sebep olmak, making the sentence Yağmur buna sebep oldu.