I am not sure I understand what you wrote after "The everlasting Father". But, I know from my Hebrew training in Jewish Temple School that the phrase means God as Creator, source of eternity and that his nature is eternal.
For a Child hath been born to us, a Son hath been given to us, and the princely power is on his shoulder, and He doth call His name Wonderful, Counsellor, Mighty God, Father of Eternity, Prince of Peace (YLT)..
"Father of eternity" is still the Father...perhaps you should change the wording again?
Holy Spirit pre-existed the incarnation as a person.
. Creation: Gen. 1:2; Psa. 104:30
The Father is a Spirit (John 4:23-24) and He is holy.
F. Jesus is not the Holy Spirit
1. The Holy Spirit is "another Comforter": John 14:16; compare 1
John 2:1.
Yet, notice how, in the context of the first verse you referenced, He says, "I will not leave you comfortless; I will come to you."
2. Jesus sent the Holy Spirit: John 15:26; 16:7.
See also Luke 23:46.
3. The Holy Spirit exhibits humility in relation to, and seeks to
glorify, Jesus (John 16:13-14).
4. The Son and the Holy Spirit are distinguished as two persons in
Matt. 28:19.
The greek word for "and" in that scripture (Mt 28:19) is "kai" which can also be translated as "even".
5. The Holy Spirit descended upon Jesus: Luke 3:22
As I have said, the Holy Spirit ascended (Luke 23:46) into eternity and also descends into time to perform His work; even into the same time frame when He was dwelling in the Son.
Was the Holy Spirit indwelling Jesus when the Spirit descended on Jesus at His baptism?
6. Is Jesus the Holy Spirit?
The Holy Spirit is "the Spirit of Christ" (1 Peter 1:11).
a. 2 Cor. 3:17: the Spirit is here called "Lord" in the
sense of being Yahweh or God, not Jesus (cf. v. 16,
citing Ex. 34:34; cf. v. 17 in the Revised English
Bible); note Acts 28:25-27, cf. Isa. 6:8-10.
So, the Holy Spirit is a different Lord than Jesus?
However, there is one Lord (Ephesians 4:4, 1 Corinthians 8:6).
So, you are saying, contrary to the Holy Spirit (1 Corinthians 12:3) that Jesus is not the Lord.
But if Jesus is the Lord and the Holy Spirit is the Lord, then they are the same Lord (Ephesians 4:5).
b. 1 Cor. 15:45: Jesus is "a life-giving Spirit," not in
the sense that He is the Holy Spirit whom He sent at
Pentecost, but in the sense that He is the glorified
God-man; and as God He is Spirit by nature. All
three persons of the Trinity are Spirit, though there
are not three divine Spirits; and only one person is
designated "the Holy Spirit."
There is one Spirit (Ephesians 4:4); and therefore if all three Persons of the Trinity are Spirit, they are the same Spirit.
c. Rom. 8:27, 34: the fact that two persons intercede
for us is consistent with the fact that we have two
Advocates (John 14:16; Rom. 8:26; 1 John 2:1).
d. John 14:18: Jesus here refers to His appearances
to the disciples after the resurrection (compare
14:19), not to the coming of the Spirit.
Jesus intercedes as the Man Christ Jesus and the Holy Ghost intercedes within us and for us as we pray for one another.
e. Jesus and the Holy Spirit are both involved in
various activities: raising Jesus (John 2:19-19-22);
Rom. 8:9-11), raising the dead (John 5:21; 6:39-40,
44, 54, Rom. 8:9-11), dwelling in the believer (John
14:16; 2 Cor. 13:5; Col. 1:27), interceding for the
believer (Rom. 8:26; Heb. 7:25), sanctifying
believers (Eph. 5:26; 1 Pet. 1:2), etc. These works
prove that the two persons are both God, but not
that Jesus is the Holy Spirit.
I agree that Jesus is not the Holy Spirit; for He is come in the flesh and the Holy Spirit is a Spirit without flesh.
However, I will say that the Holy Spirit is "the Spirit of Christ" (1 Peter 1:11); whom He released from His human body at the juncture of Luke 23:46.
G. The Father is not the Holy Spirit/(Ghost)
I will also agree with you there (that the Father is not the Holy Ghost) but will contend that there is a sense in which the Holy Ghost is the Father.
But you would have to read what I have already written in this thread to be able to get an understanding of what I mean by that.