"What other books are you reading?"
Translation:Başka hangi kitapları okuyorsun?
If I remember correctly 'diğer' is used when you mean a specific other and 'başka' is used when you do not have a specific alternative in mind.
'diğer restorana git' / 'go to the other restaurant' e.g you have a concrete other restorant in mind 'başka restorana git' / 'go to another restaurant' e.g you don't have a specific alternative in mind... just go somewhere else
I am sure there are people who know the correct grammar lingo for this but this is as good as İ can explain.
When you say “Hangi başka kitapları okuyorsun", it sounds like you are reacting to a previous statement, if that makes sense. Example: -Başka kitaplar da okuyorum. (I read other books as well) +Hangi başka kitapları okuyorsun? (What other books are those that you are reading?)
You need a verb there. And instead of ne, "hangi" is used. So your sentence would be like: Hangi diğer kitapları okuyorsun? But if you say it like this, it kinda sounds like you are reacting to a previous statement: -I don't read this, I read other books. +What are those other books that you are reading? (Hangi diğer kitapları okuyorsun?) So "başka hangi kitapları okuyorsun?" is a better translation.
Yes, but the problem is you cannot use "ne" as a question adjective. To use ne in this sentence, you should use it as a question pronoun: Okuduğun diğer kitaplar neler? It is the same in the sentence you wrote. Ne yemek istersin? Ne is a pronoun here. It would be clearer if you think it as "neyi yemek istersin?"