Learn Turkish: Çocuk nasıl da büyümüş, ne kadar da olgunlaşmış! - How the child has grown, and how much he has matured!

Adding da to question words like nasıl (how) and ne kadar (how much) turns them into exclamatory intensifiers. Instead of asking a question, it expresses strong emotion or amazement. Without da, Çocuk nasıl büyümüş? would be a genuine question meaning "How did the child grow?" But nasıl da büyümüş! means "How he has grown!"

Is there a difference in meaning between nasıl da and ne kadar da here?

They are very similar in this context and both express amazement. Nasıl da emphasizes the manner or the sheer fact of the action, while ne kadar da specifically emphasizes the extent or degree. They are often used together in parallel structures like this for a stronger emphatic effect.

Why are the verbs in the -mış past tense instead of the definite past tense (-tı)?

The -mış tense is not just for hearsay or reported past; it is also used to express sudden realization or surprise upon noticing something. In this sentence, the speaker is likely seeing the child after a long time and is expressing their immediate astonishment at the change. Using büyüdü would state a dry fact, lacking that element of surprise.

How does the verb olgunlaşmış break down?