The topic of nominal sentences like this was discussed recently in the weekly Hawaiian language column Kauakūkalahale. (17 November 2018 "Ili ka waʻa ma nā kapakai o Punipainu" by Laiana Wong) Original Hawaiian used a great deal of nominal sentences instead of sentences with verbs as my alternative is.
"What" is "he aha." "He aha ke kinipopo kou makemake," I believe is the appropriate translation for "what ball do you want." The word "hea" is the giveaway for using "which," a choice between known items. "What ball do you want?" implies an open ended question where the answer could be baseball, red ball, large ball, their ball, etc. It is a fine point, I suppose. Hope this helps.
"He aha ke kinipopo kou makemake." is not a grammatically correct sentence. What ball and which ball mean the same thing in English, which ball being standard English and what ball being colloquial. That said, it appears that you are trying to conform Hawaiian syntax and lexical choice to English thought, which you should not do.
The word aha really means what and the word He means a. Your question would read literally A what the ball your desire? You do not need He (a) and ke (the) in there at the same time.
That cannot be done. Which or its colloquial alternative what is used as an interrogative adjective modifying the noun in question. Hawaiian language simply does not use their interrogative pronoun "what" ( aha ) as an adjective in the same way that English does. One step of learning a new language is to get away from trying to make the new language fit into one's mother tongue. Hawaiian and English have drastically different language rules.
What ball do you want? and Which ball do you want? are both "ʻO ke kinipōpō hea kou makemake?" Another example of what I am saying is that the word "want" in English is a verb but in Hawaiian the corresponding "makemake" is used as a noun. Step away from English completely as possible is my recommendation.
Based on all the conversation below, there is a lot of accumulated knowledge here. But i have a much more basic question so please forgive my ignorance (i'm having a lot of trouble with Hawaiian). I don't understand why this sentence needs the " 'o" before the "ke kinipopo". I thought the " 'o" was for people. Thanks in advance.
It's a similar use but a bit more expanded. It depends on the place in the sentence. Rather than a long explanation, here are some examples. The type of sentence in the prompt has no English style verb, but instead the first half of the sentence is a sort of predicate that still follows the VSO nature of the language. The second part of the sentence is the subject. Understanding ‘o for the initial predicate versus the subject position is the key.
When the first half of a verbless sentence is a definite noun, it starts with ‘O regardless what kind of noun it is.
1) 'O Keoki ke kumu. The teacher is Keoki. ( or Keoki is the teacher. )
2) ‘O ke kumu ka wahine. The woman is the teacher.
If you are dealing with the second position (subject) whether there's a verb or not, the word ‘o is used only for proper nouns, not always people, just names.
1) He kumu ‘o Keoki. Keoki is a teacher.
2) He kumu ka wahine. The woman is a teacher.
3) ‘Ai ‘o Keoki i ka mai‘a. Keoki eats the banana.
4) ‘Ai ka wahine i ka mai‘a. The woman eats the banana.