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Hi Hannah,
These sentence structures are commonly used in daily speech.We use them to emphasize that WE DON'T CARE or IT DOENS'T MATTER what happens, who does something, what you do etc, because it does not change the situation or your intention.
Let's use your sentences to explain how it works,
谁有问题谁问。Anyone have any questions, Just ask! (Repeat 谁 twice to emphsize that it does not matter who ask questions)
有什么吃什么。Eat whatever we have. (Repeat 什么 twice to emphsize that we don't care what to eat)
你想去那儿就去哪儿。Go wherever you wanna go. (哪儿。。哪儿 is used to say that I don't care where you go)
你怎么说，我就怎么办。I'll do whatever you ask me to! (Here this structure is used to say that it is not important to say exactly which.)
As you can see, that people use ANY, ANYTHING, ANYONE, WHOEVER, WHATEVER, WHEREVER in English language to express the same thing. In Chinese language, we can use this structure to do the same job.
Keep asking me if anything is not clear to you. 啥不懂接着问啥：-)
