Learn Turkish: Su bu kadar hızlı nasıl buharlaştı? - How did the water evaporate so fast?

In Turkish, the word you want to emphasize goes immediately before the verb. Question words naturally seek the most important new information, so they usually sit right in this pre-verb "focus" spot. Putting nasıl there emphasizes that you are asking how it happened.

What is the root of buharlaştı and how is the verb built?

The root is buhar, meaning "steam" or "vapor". The suffix -laş (or -leş) is used to turn nouns or adjectives into verbs meaning "to become [that thing]." So buharlaşmak literally means "to become vapor." The -tı simply adds the past tense.

Why do we use bu kadar hızlı instead of just çok hızlı?

Çok hızlı just means "very fast." Bu kadar hızlı translates to "so fast" or "this fast" (literally: fast to this extent). When you are pointing out a specific degree of something or expressing surprise at it, bu kadar is the more natural choice.

Could I use the irreversible action pattern from this lesson here, like Buharlaştı o buharlaşış?

You could use that pattern if you were making a dramatic statement—meaning "It evaporated, and that was that (it was gone for good)." But because this sentence is a genuine question asking for the method or reason it vanished, we stick to the standard simple past tense verb buharlaştı.