As Members of the Church of Jesus Christ of Latter Day Saints is it okay to have questions about the gospel, the prophet, the leaders? I would say most definitely yes...in fact, it is spiritually healthy to ask questions but please hear me out and keep reading.
One main purpose of this life is to become an agent to ourselves. Agency is essential to our eternal identity and honestly we could not make it to the greatest kingdom without it. Also remember that was the difference in the plan that was rejected and the great plan that was accepted. In order to be an agent to ourselves we do need to understand what we are choosing and why.
But as we ask questions lets look to the scriptures to two examples of brothers, raised in the same household who also asked questions but did so with different intents and with different outcomes. Lets think of Nephi vs Laman and Lemuel who were all faced with their father's, the prophet's, counsel to leave their familiar and comfortable home and go into the wilderness and face some hefty obstacles. I can't even imagine how hard this decision would have been. I am sure we only know a tiny part of what they suffered.