Questions & Answers about Bu kural hakkında ne düşünüyorsun?
Since the current lesson is about göre, can I say Bu kurala göre ne düşünüyorsun?
No, because göre means 'according to' or 'based on'. Bu kurala göre would mean 'according to this rule' (for example, 'According to this rule, we can't do that'). To ask what someone thinks 'about' a topic, you need to use hakkında.
Does hakkında require the dative case on the noun like göre does?
No, it doesn't! Unlike göre, which always needs the dative case (like kurala göre), hakkında just follows a plain noun. That's why it is simply kural hakkında. Note that personal pronouns do take the genitive before it, like benim hakkımda (about me), but plain nouns do not.
In English, we say 'What do you think?', not 'What are you thinking?'. Why does Turkish use the continuous -iyor tense here?
Turkish uses the present continuous (-iyor) for many things that English treats as simple present, especially for current opinions, feelings, and thoughts. By asking ne düşünüyorsun, you are asking for their opinion at this very moment.
Why is the question word ne (what) placed right before the verb?
In Turkish, the most emphasized information in a sentence is placed immediately before the verb. In a question, the question word itself is usually the most important piece of information, so it naturally sits right next to the verb.