Following a faith means always "being a child" to it. Once you ask no more questions of your guru, book, peer, authority, and elder, you're not really following the teaching. Mystic experiences, god, so have you are not understood in and of itself. So, here's something I like (I consider myself spiritual but not religious-take as is or for conversation)
Don't search for the answers, which could not be given to you now, because you would not be able to live them. And the point is, to live everything. Live the questions now. Perhaps then, someday far in the future, you will gradually, without even noticing it, live your way into the answer.
Letters To A Young Poet - #4
Maybe the point isn't to ask physical questions "does god exist" but live the questions (the mystery/god)-ask by your actions not by your words. Only when you live mystery, mystic, holy spirit, god, so have you, you can still ask questions (and should) just change your perspective-it's not about doubt and ignorance but interest to increase your understanding and living your faith.
I never heard of any wise person who did not ask questions as a wise person. If anything, they ask more questions because the child feels he doesn't need to which makes him have ego as if he doesn't need to advance to be spiritual lead. He mistakes asking questions in doubt rather than asking questions for wisdom.
Don't use teachings and people as idols and you won't feel uncomfortable about questioning.
Also, change your perspective about spirituality and religion. The wise doesn't differentiate but takes every other person's views into consideration and reflection (and maybe an answer) to his own inquisitive nature.