This has been a major misconception in Muslims around the world that they are not allowed to ask question about things mentioned in Quran. I would like share few references of Prophet Ibrahim (Abraham) (A.S) from Quran who was great critical thinker and Khalil (friend) of Allah.
Have you not considered the one who argued with Abraham about his Lord [merely] because Allah had given him kingship? When Abraham said, "My Lord is the one who gives life and causes death," he said, "I give life and cause death." Abraham said, "Indeed, Allah brings up the sun from the east, so bring it up from the west." So the disbeliever was overwhelmed [by astonishment], and Allah does not guide the wrongdoing people.(Quran- Surah-Bakarah, Verse -258)
And [mention, O Muhammad], when Abraham said to his father Azar, "Do you take idols as deities? Indeed, I see you and your people to be in manifest error."
And thus did We show Abraham the realm of the heavens and the earth that he would be among the certain [in faith]
So when the night covered him [with darkness], he saw a star. He said, "This is my lord." But when it set, he said, "I like not those that disappear."
And when he saw the moon rising, he said, "This is my lord." But when it set, he said, "Unless my Lord guides me, I will surely be among the people gone astray."
And when he saw the sun rising, he said, "This is my lord; this is greater." But when it set, he said, "O my people, indeed I am free from what you associate with Allah .
Indeed, I have turned my face toward He who created the heavens and the earth, inclining toward truth, and I am not of those who associate others with Allah ."(Quran- Surah-Ibrahim, Verse- 74-79)
When he said to his father and his people, "What are these statues to which you are devoted?"
They said, "We found our fathers worshipers of them."
He said, "You were certainly, you and your fathers, in manifest error."
They said, "Have you come to us with truth, or are you of those who jest?"
He said, "[No], rather, your Lord is the Lord of the heavens and the earth who created them, and I, to that, am of those who testify.
And [I swear] by Allah, I will surely plan against your idols after you have turned and gone away."
So he made them into fragments, except a large one among them, that they might return to it [and question].
They said, "Who has done this to our gods? Indeed, he is of the wrongdoers."
They said, "We heard a young man mention them who is called Abraham."
They said, "Then bring him before the eyes of the people that they may testify."
They said, "Have you done this to our gods, O Abraham?"
He said, "Rather, this - the largest of them - did it, so ask them, if they should [be able to] speak."
So they returned to [blaming] themselves and said [to each other], "Indeed, you are the wrongdoers."
Then they reversed themselves, [saying], "You have already known that these do not speak!"
He said, "Then do you worship instead of Allah that which does not benefit you at all or harm you?
Fie upon you and to what you worship instead of Allah . Then will you not use reason?"(Quran-Surah, Verse-52-67)
So point is Islam encourages you to ask questions and ponder upon different things with open mind but you should focus in the right direction and ask relevant questions. For example in story of Prophet Yusuf(Joseph)(A.S) in Quran, there is only mention of interaction with Father Yaqob(Jacob) (A.S) and his brothers, there is no mention of his mother. So someone would ask what his mother was doing in all this situation? This is kind of irrelevant and Allah wants you to focus on things mentioned in story of Yusuf (A.S)
Lastly there are also some verses and authentic hadiths which speaks about asking less questions. That principle was in effect only when Quran was being revealed. Now, it is in complete form, so we can ask questions in order to give strength to our Emaan.
Thank you for your time. If you are confused about specific issue or want to talk about anything related to Islam, you can mention them in comments and i'll try to address them in upcoming posts.