Why did God choose to keep Himself, hell and heaven and angels hidden from human eye?
The angels, heaven, Hell and the reality of sin and reward remaining hidden from human eyes are meant to prepare ground for test and of human beings because if the curtains or the barriers are removed and if the unseen matters are seen, then it would be meaningless to believe in God and the Hereafter.  that is because belief in God and the Hereafter means accepting things tribulation which are not perceivable through the senses. Thus, in the holy Qur’an, belief in the unseen is considered to be one of the signs of believers. 
Experience tells us that seeing the unseen has not so much impact on people. There were many people in the time of the Holy Prophet (PBUH) seeing his miracles, yet they did not tend to embrace the truth and the religion of the Prophet (PBUH). When it comes to strengthening Muslims' faith, it generally does not have a lasting impact on them. Many instances of the exposure of the unseen have been witnessed in the history where the impact had been momentary. For instance, Banu Israel saw many miracles; they saw the river split into two and which they crossed on foot but they began to worship the calf soon after. Also, miracles and virtuous acts which have been seen from the prophets and infallible Imams (A.S) did not have a lasting impact on the general public. Only few people who were misled due to ignorance, were guided in the right path.
Therefore, the best way to increase and strengthen faith is to benefit from the blessing of intelligence and to think about the world and to resort to servitude to God, the Exalted as evidenced and recommended by the Qur’an and prophetic traditions. Of course, paying attention to the sayings and advice of the infallibles will also be greatly helpful.
 On the day when some of the signs of your Lord shall come, its faith shall not profit a soul which did not believe before, or earn good through its faith. Say: Wait; we too are waiting." Al-An'am, 158.
 "Those who believe in the unseen…" Al-Baqarah, 3.
 Vide: Strengthening Faith and Beliefs, question 9323; "Ways to Strengthen the God-seeking Sense", question 3472.
Why should we worship Allah?
What Is The Religion of Allah?
Three Parts of the Religion of Allah
Monotheism (Is Obedience a Negation of Man’s Freedom?)
Resurrection and Final Assemblage
Role of the Qur’an in Imam Reza’s life (Part 4)