I’ll consider three interpretations of your question. I’m pretty sure you are thinking of the third, but the other two are useful for building up to give the final answer.
- "God's view" is not part of a formal system.
If the question is about non-formalized natural language, then there is no problem with allowing X (God’s frame of reference) to contain X. For example, we can talk about “everything”, which includes the concept of “everything”, without problems. We only have paradoxes resulting when we treat language and the objects language refers to formally.
- "God's view" is an object language in a hierarchy
Since your question refers to a frame of reference Y which is necessarily outside the frame of reference X, I assume that you are asking about formal systems. You are correct that this is exactly how formal systems are typically set up in order to avoid problems such as Russell’s paradox. As Not_Here points out in the comments, Y is the “meta-language” of the formal system, while X is the “object language”. Y can also be treated as an object language by a higher level meta-language Z, and this hierarchy goes up forever. In this framework, your “unanswerable question”, which I take to be “Where is the truth of X derived from?”, is not only unanswerable but also unaskable. That is, the question is not well-formed within the object language for X. Viewed in this way, your unanswerable question is similar to the liar’s paradox, which analyzes the sentence “This sentence is false.” If that sentence is true, then it must be false (because it says so), and if it is false, then it must be true (because it is false that it is false), so we have a contradiction. The solution is that the truth of any sentence in the object language X can only be asserted or denied in the meta-language Y.
- "God's view" is the entire hierarchy of all meta-languages
Since you set up your question with X being God’s view, you probably have the idea that there is no meta-language Y above X, but rather that X actually contains the entire hierarchy of languages all the way up. This is also legitimate in standard treatments of formal languages. Frames of references are usually formalized as sets in set theory. There is no set of all sets, but we can still talk about the class of all sets without any problems. The only issue is that the class of all sets is not a set and therefore is not part of any of the object languages in the hierarchy. So again questions about X (the class of all sets) can not be written in the language, so they are actually unaskable in addition to being unanswerable.
All of this is a description of what is typically done in formal systems. These systems are known to be consistent and to capture all of mathematics. Your observation of unanswerable questions is a good criticism of naive semantics for language, and observations like it are part of the reason that these hierarchical formal systems were developed instead.