I couldn't resist.
I have a question to address to the op well instead of an answer.
Trinity - 3 parts right?
Son - Physical yet diety
Holy Spirit - Spirit
Where does that leave the Father?
John 4:24
God [is] a Spirit: and they that worship him must worship [him] in spirit and in truth.
If Father is a Spirit, then isn't He holy? If He is holy then isn't He the Holy Spirit? But if Holy Spirit is the third part of the trinity we are back to square one on defining who the Father is.
Now some answers:
What do you believe about the Holy Spirit?
Holy Spirit is the complete Spirit of God like Georges explained.
Who or what is the Holy Spirit if you do not believe it is God?
I believe Holy Spirit is God's Spirit, not a seperate part of God.
In what way is the Holy Spirit not God?
In what way is my flesh not human? There isn't a way where Holy Spirit is not God. It is God's spirit. Not a seperate God.
If Jesus is physical then why does Jesus say what he said in John 4:24? Well if you say he put on flesh but before that he was spirit then were there 3 spirits in heaven? Father spirit, Son spirit and Holy spirit? What say JG? You seem to be counting only one spirit? Right, this is where you need the spin that says all three spirits are one. Grabs some of your popcorn