Are the Father, Son, and Spirit three separate spirits and souls or one spirit and soul?
A soul is the life principle of a bodily being. Man is the only bodily being with a spiritual soul, meaning we are the only bodily beings who are both made in the image and likeness of God (Gen. 1:26-27) and whose souls are undoubtedly immortal. For more on the human soul, see the Catechism of the Catholic Church (CCC) 362ff.
In contrast, angels are pure spirits but created ones.
The Father, Son, and Spirit are each distinct, uncreated spirits, and it’s important to emphasize distinct rather than separate. They each wholly possess the same divine nature, united in the Holy Trinity. So we have one God, because they wholly possess the same divine nature, and yet they are three distinct, divine persons. Of course, only the Son became man, so he also has a human soul and body.
For more on the Trinity, see CCC 232ff.
By Tom Nash