"America" should have a capital A. Other than that, it is grammatically correct.
But I don't think that's what you want to say. The question,
Why does he have to be from America?
means that you know that he is from America (that is, America is his home), and you want him to be from somewhere else. That kind of question is often used when someone is sad that a person is from somewhere else because they want to have a romantic relationship with that person. But a native English speaker might be able to figure out that is not what you really mean...
Just like me: I don't think that's what you mean. It sounds like you don't understand why the caption says "He must have returned from America" and you want to understand.
In that case, you could ask,
Why do you think he returned from America?
Keep in mind that it could be a joke. In that case, you could simply say,
I don't get it.
Which means you don't understand the joke, and maybe someone will explain for you.
Both "I won't be needing that" and "I don't need that" are grammatical.
The problem with your teacher's logic is that "need" is not a modal in either of those. Two easy-to-detect signs of modality are:
- They have the syntactic properties associated with auxiliary verbs in English, principally that they can undergo subject–auxiliary inversion (in questions, for example) and can be negated by the appending of not after the verb.
- They do not inflect (in the modern language) except insofar as some of them come in present–past (present–preterite) pairs. They do not add the ending -(e)s in the third-person singular (the present-tense modals therefore follow the preterite-present paradigm).
Wikipedia
For the first point I listed, it should be pretty obvious that not does not follow need in "I don't need". For the second point, since people say "he needs...", we know it's not modal in this sense either.
"Need" specifically is a semi-modal. Your sentence needs modification were it to use need as a modal:
I need not have help.
According to the statistics here, the modal form of need is not used very often in American English (which is why I think it sounds old fashioned). A COCA search for BE needing (capitalizing "be" means it matches all forms of the verb, such as be, were, 're, etc.) returns 356 results, so I think it's safe to say that educated speakers do use "will not be needing" and similar (I would).
Best Answer
The idiom is "The key to something", with "to" being a preposition, used idiomatically instead of "for". So we say "the key to the door" or "the key to my heart".
So after "the key to ..." we need the object of the preposition "to", this can be a noun or a gerund, but not a verb. So "The key to having..." is correct, "the key to have...." is not correct.
Don't think that "to" always marks an infinitive. Sometimes it is just a preposition.