The doctrine as believed by the reformed community is specified in the Westminster confession: "In the unity of the Godhead there be three persons, of one substance, power, and eternity; God the Father, God the Son, and God the Holy Ghost. The Father is of none, neither begotten, nor proceeding: the Son is eternally begotten of the Father: the Holy Ghost eternally proceeding from the Father and the Son." This is what I believe. The RCC agrees with this assessment.
1.) In your confession, which Greek word has the same definition as "begotten"?
For example, is it the Greek word gennaō...
Hebrews 1:5... For unto which of the angels said he at any time, Thou art my Son, this day have I begotten (gennaō) thee? And again, I will be to him a Father, and he shall be to me a Son?
2.) In your confession, does the word "begotten" refer to incarnation?
Luke 1:35 ASV... And the angel answered and said unto her, The Holy Spirit shall come upon thee, and the power of the Most High shall overshadow thee: wherefore also the holy thing which is begotten (gennaō) shall be called the Son of God.
Luke 1:35 KJV... And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born (gennaō) of thee shall be called the Son of God.
Here is a concise statement of what I believe...
The spirit Yahweh is the only one who is eternal. Yahweh is also in the universe as spirit and as a human. Yahweh in the universe as spirit is called the Spirit of God, Yahweh in the universe as a human is called the Son of God, and eternal Yahweh is called God the Father.
And here is a more detailed overview...
(Note: I agree with the view of Melito, Bishop of Sardis around AD 160-180. The following is how I word it.)
For this creation, Yahweh God (the only one who transcends all creations) determined to create a universe with a kingdom of redeemed humans (living souls) for his glory where he would reign as a living soul himself. The Scriptures describe how Yahweh would accomplish his plan. In an instant, transcendent Yahweh (called God the Father) created the supernatural and space-time of this universe and also became immanent as a spirit (called the Spirit of God) and in the form of a living soul (called the Son of God) with a glorious human body. God the Father then created all things within the universe by the power of the Spirit of God commanded by the Son of God. But whereas Yahweh created a human spirit and soul for each of us, Yahweh himself became the human spirit and soul of Jesus. At his conception, Jesus' glorious body was changed to a mortal body to be made like us so he could make reconciliation for our sins. At his resurrection, Jesus' mortal body was changed back to a glorious body and he will also give each of his elect a glorious body when he returns to reign in his kingdom forever.