Faith and intuition.

I found a contradiction in my perceptions.
 
On the one hand, it is clear to me that emotional faith in G-d or the Torah is not enough and a person must challenge themselves, ask questions, and examine with their minds what the truth is.
 
 
On the other hand, there are parts of my life that I have no intellectual evidence for and I simply believe in them.
 
1. My mind, my trust in my mind that it works well most of the time, is faith without any intellectual evidence.
 
2. That there is objectively valid morality. That there are things that are right to do and some that are not. What is required by this command is my belief in the command. I have no ability to prove it. It is a strong feeling.
 
3.
Free choice, I just feel like I’m choosing, I have no evidence that I’m choosing.
 
 
So I’m trying to understand the place of emotion and the concept of faith. I guess it’s related to understanding the concept of intuition.
 
Can you direct me?
thanks.