I have a number of questions concerning the nature of our Lord Jesus Christ:
Can our Lord Jesus Christ and the Holy Spirit be referred to as Creator like the Father?
Has our Lord Jesus Christ existed from eternity, or just at incarnation?
Did our Lord Jesus Christ exist as human and Divine before the incarnation as well?
Do the members of Trinity have separate functions or do they sometimes work together, sometimes exclusive. For example, the death of our Lord Jesus Christ wasn't the death of the Father or the Spirit?
No doubt God the Father is the creator, however it is through the Son, the Word that God created the world, "Then God said, "Let there be light"; and there was light" (Gen 1:3), "All things were made through Him (Jesus Christ), and without Him nothing was made that was made" (John 1:3), "For by Him all things were created that are in heaven and that are on earth, visible and invisible, whether thrones or dominions or principalities or powers. All things were created through Him and for Him" (Col 1:16).
God the Father created the whole world through the Son, He created it with His reason, His Word i.e. the Second Person of the Trinity. Therefore St. Paul says "has in these last days spoken to us by His Son, whom He has appointed heir of all things, through whom also He made the worlds" (Heb 1:2). So we can say that Lord Christ is the Creator. He created with the power of His Divinity, being the Second Person; the Logos; the Wisdom and the knowledge of God.
The Holy Spirit was also at the creation "And the Spirit of God was hovering over the face of the waters" (Gen 1:2).
In many occasions we see the three Persons of the Trinity working together or at times One is manifested more in His own role. Christ, the Son is the One that died on the cross, but Christ is God incarnate.
The name Jesus means "the Savior", which is an attribute of the Son. The Son existed from the beginning in His divine nature. He is rightly called the eternal offspring of the Father. He is God's offspring, and as being the proper Son of God who ever exists; He exists eternally.
However the human nature of Christ was not from the beginning otherwise His birth from St. Mary would have been superfluous. St. Paul said that the Lord came to give aid to us:
"Therefore, in all things He had to be made like His brethren" (Heb 2:17) and to take a body like ours in order to offer it for us as His own.