Q. How is faith possible if one’s reason is uncertain about its claims?
A. I have abbreviated your question but this is the gist of what you ask. What faith is saying is that reason is a great pointer to truth but not the only one. There are realms beyond and above reason. Reason works with the mind; faith works with the soul.
The relationship of faith and reason is described in these words by the Chazon Ish (Rabbi Avraham Yeshayahu Karelitz), the great sage of the 1st part of the 20th century:
If a man is spiritual and his eye is bright with the glory of the sky above and the earth below, he becomes moved and enraptured with the marvellous and insoluble riddle of the world. When the intelligence of man sees at last the truth of God’s reality, blessed be He, at once an infinite joy enters into the man and his gladness is a delight. When a man rises to such heights of holiness, a new world is revealed to him, for the possibility is given to a man in this world below to be as an angel for a moment and to enjoy the Holy Glory. All the pleasures of the world below are as nothing compared to this pleasure of a man cleaving to his Creator, blessed be He.