The answer reverses the phrasing. This is intentional yeah?

I'm pretty sure "想" should also be allowed here in lieu of "要". Reported.

Same

I don't think omitting the second wo3 is a mistake

Is it possible to embed the pop up dictionary in the example sentence that is displayed when the user can't answer the question?

Native speaker here. The 因为 at the start is not necessary and is not said in common speech because the 所以 already implies the part in front is a reason.

"I want to go" in Chinese is "我想去"， "我要去" means "i have to go" MISTAKE here, folks. im a native chinese speaker

要 seems like a bad choice for this, since it makes the sentence "because Im going to china" 想 would be better

我是为了去中国而学中文的。

学 is enough by itself.