I want to verify about the Trinity as one God but 3 separate distinct persons, how about this 3 persons of their spirit being identity? Are they 3 spirits? As for the Son his spirit is enclosed by flesh...
Here's the way I would phrase it:
There is one God in terms of being or essence, yet three distinct Persons, in terms of personhood, Father, Son, Holy Spirit. There is one "what" and three "who's.
In regards to the unity or oneness of God, he is one in terms of essence, so there is only one spirit.
Let me use a human comparison. If there was a human being like God, which there is not, there would be three distinct Persons sharing one body. The body is the essence.
God does not have a body; he is spirit. Therefore, there is only one spirit.
The Holy Spirit is a distinct Person, just like the Father and the Son.
Also, theologians prefer to use the word "distinct" rather than "separate" when discussing the three Persons. This is because the word "separate" is a spatial term, and God is not a spatial being. He created the laws of space and time, and is not constrained by the dimensions within space or time.
Some Christians have this idea that God is like a man, in that he is constrained by space and time, however this is not correct. God created all those things, therefore he is above them.
Man is created in the image of God in the sense that he is meant to reflect God's holiness and to rule over creation like God rules over all things. He is God's representative in the material realm. This does not mean that God has a body or form shaped like a man, though.
If you consider our bodies, they are meant to operate in the physical realm. For instance, we have hair so that we can keep our heads warm. We have fingers to pick up small objects. We have legs to walk around, and sexual organs to procreate. We have noses to breathe oxygen. God doesn't have these needs. He is the creator so he is not dependent upon the creation. He has no needs.
It is true, though, that Jesus has a glorified body but he is a union of God and man. He has two natures. He is God, but he is also man. And he has a human body due to the fact that he is fully man. But, he is fully God at the same time.
Jesus isn't a spirit simply enclosed with flesh. He is man by nature, as well as being God by nature.
In the OT there were theophanies and Christophanies where God appeared as a man in a body that appeared human. Jesus was more than that. His body is a real human body just like any other man. But, he has a dual nature being God as well.
The guys who believe God is like a man in this way rely on Scriptures that seem to indicate this, but they don't understand that God uses language so that we can relate to it. This is called "language of accomodation".
Consider how we talk to our babies. We don't use complicated language to explain difficult things. We use simple language and baby talk. God basically uses baby talk when communicating with the spiritually immature. He then expanded this complexity after the resurrection through men like the apostle Paul.
For example, in Genesis 8:1, it says that God remembered Noah. Well, it's obvious that God didn't have a "senior moment" and forget Noah in the Ark floating around. Scripture uses language of accomodation sometimes so that man can relate to God.