Gödel's Incompleteness Theorem (roughly) states that in every logical system, there are truths that cannot be proven. Most people don't extend this to philosophy, but if you want to be entirely formal - yes, there are questions that we ("we" being the entire universe) will never be able to prove, or know.

I would say that Gödel theorems apply to the questions you asked as well. For example, consider the question "What is the meaning of life?" Most of us would say we haven't got a clue. The Christians might say, "to get into heaven" or "to worship God" (introducing an element beyond our current logical system). But then the question can be asked "what is the meaning of God's life?" or "Suppose we reach the ideal state, in heaven, what is the meaning then?" and there will never be an end to the question. It's the same with God (or metaphysics in general). Suppose you discover a valid theory of metaphysics -- what of meta-metaphysics? And then, what about meta-meta-metaphysics?

As for the question of morality, there we might have some success. It might be possible to discover what kind of behavior truly results in optimal happiness and advancement for the human society, and model our ethics on it (really, that's what most philosophers attempt to do).