Is One Allowed To Question G-d?

I can prove from last week's parsha, Beha'alotcha, that one is, indeed, allowed to question G-d.

As we see in Bamidbar/Numbers 11:21-22, Moshe question's G-d's ability to provide enough meat to feed the Children of Israel.

This is all rather reminiscent of Melachim/Kings II, Chapter 7, wherein Elisha's prophecy concerning the abundance of food is questioned by "the man on whose arm the king leaned".

The man is trampled the next day by the hungry mob.

In Sanhedrin Heilek, this is held up as an example of G-d acting middah k'neged middah - measure for measure - punishing and rewarding people for their actions according to their actions, sometimes what we might call "ironic".

Rashi asks (regarding Moshe's comments) "Which was the more severe sin, this, or 'Listen now, rebels' (Which is the prelude to the rock-hitting incident of Bamidbar/Numbers 20:10) ?"

He then quotes Rabbi Akiva on the issue as saying that the difference between this and the rock-hitting incident is its private nature. Moshe did not publically express his doubt in the Omnipotence of G-d, so he was not punished.

This gels nicely with the Elisha story as well.

What we have learned: It is okay to, yourself, doubt Jewish dogma.

Now, for the better I might argue, we live in a day and age in which people are not smote for their sins. This is to allow humans true free will, as Rabbi Berkovitz might tell you. Indeed, the doctrine of hester panim is widely accepted in Orthodox circles to various extents.