Is it wrong to question God?

Well... most Christians would answer a vehement 'YES!' to this question, and are they wrong? No, not entirely, but they are not fully informed either.
This is as much the failing of their ministers as it is their own.

If you are questioning God because of doubt about his power, wisdom and foresight, then yes. Plain and simple. You are absolutely wrong in questioning him. For those of the faithful, your faith is flawed.
Just to be clear, I am not speaking of atheists here, they are a different discussion altogether. I suspect the Agnostics will appreciate some of what I have to say, however.

To any person of faith, with a little critical thinking, it should be apparent that the Intelligence, wisdom, power and foresight of the Holy Father are far beyond any capabilities in those areas that humans may achieve.

And so, in that context, questioning our creator is arrogant, prideful and ignorant.

However, there is a flip side to this coin. To borrow an idea from the late George Carlin, it's the context that counts. We have already established that from a Human perspective, God has power, intelligence, wisdom and foresight far beyond human capabilities, ergo, from the general perspective of our level in comparison to his; Infallible.

If we look at the concept of questioning God from the perspective that we exist today primarily for the purpose of learning, growth and overcoming ignorance, and we question God solely with the intent of trying to better understand his intent, viewpoint, purpose and goals, is questioning him wrong in that context?

I suspect, for many people, that one answers itself.

I pray that this information brings some clarity on an old, but widely misunderstood topic.