See, there you are confusing a man's spirit with the Holy Ghost.
All men have a body, soul, and spirit. Since Jesus was a human being, He had a spirit, soul, and body. That has NOTHING to do with the Holy Ghost.
1 Thessalonians 5:23
And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ.
No, the "Father" doesn't "have a spirit" per se. Rather the Holy Spirit comes forth from the Father, just as the Son does. They are one but distinct. As you've been shown many times.
John 15:26 But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me:
John 16:27 For the Father himself loveth you, because ye have loved me, and have believed that I came out from God.