These are all very important functions of the human brain. Being born and raised in the Mormon Church, I grew up not realizing the importance of thinking, examining, and analyzing. Being told, in essence, that I should not examine or analyze beliefs of the Mormon Church is not only wrong on many levels, but it is also very debilitating. People must be able to think critically, examine closely, and analyze fully whatever they feel is necessary to confirm realities in their lives.
Curiosity is a natural state which, in my opinion, should be encouraged. A person's natural curiosity in conjunction with imagination and intelligence is what makes life vital and interesting - and feeling trapped in a world where your natural curiosity is squelched and stifled, where your innate intelligence is not applauded, and where your ability to think critically and analyze situations is not only discouraged but also practically prohibited, is tantamount to holding a person's brain in prison.
So it is with religion, and in particular, Mormonism. Faith is all fine and good - but when the facts contradict those things that "they" tell you are true and what you "should" believe, it's not called faith anymore, but rather denial. I spent so many years in the chains of denial that I felt like I was living in a tunnel with no light anywhere to be seen. But when I finally began to examine and analyze my "beliefs," I discovered that what I had believed in for so many years was actually false - and not only did light finally appear at the end of the tunnel, but the house of cards constructed so carefully by Mormonism came tumbling down in my mind.
And now I am breathing free - able to think, examine and analyze - and then to accept or reject what I discover on my own terms. Living an authentic life truly is its own reward.