The doctrine of the Trinity teaches that God is one, and God is three (Father, Son, Holy Spirit.) From what I understand the Eternal Son came in human flesh, and we know that resultant man as Jesus of Nazareth. So would it be accurate to say God the Son was operating in a human body as "Jesus"? Were the Father and/or Spirit also in Him?
(I am, of course, looking for answers from a Trinitarian perspective.)
All three persons of the Trinity are in a perichoretic union.1 Hence, the Holy Spirit is called the Spirit of the Father2 and the Spirit of the Son,3 yet there still exist three persons of the Trinity.4
The Son said, “I and my Father are one,”5 to which the Jews picked up stones in order to stone him. He also told Phillip, “I am in the Father and the Father is in me.”6 By means of the Holy Spirit, the other Comforter,7 the Father and the Son would dwell in individual Christians.8
The Father is essentially and spiritually (obviously, not physically, as in the sense of a corporality) in the Son, as the Son is spiritually in the Father, and both are spiritually in the Holy Spirit, as there is a unity of essence. In such a manner, the Father is indeed in the Son, not only by a unity of will, as some assert. Thus, the apostle Paul wrote that “God was in Christ, reconciling the world unto Himself.”9
1 From the Greek word περιχώρησις
2 Matt. 10:20 cp. Mark 13:11
3 Gal. 4:6
4 Matt. 28:19
5 John 10:30
6 John 14:10–11
7 John 14:16
8 John 14:23
9 2 Cor. 5:19
Jesus is one Person of the Trinity. He is never the Father or the Spirit. That being said, Jesus did speak of the union He had with the others when He said "the Father was in Him" and such. However, it was the Son who became a Man--not the Father or the Spirit.
In that day you will know that I am in My Father, and you in Me, and I in you. John 14:20 NAS
The Father and the Spirit are spirit and do not have physical bodies, so neither of them could be physically in the body of Jesus.
I will answer your second Question only because the first seems very complicated and technical.
Were the Father and/or Spirit also in Him?
Answer: yes the Holy Spirit was in Him, no the Father was not in him (he was in Him in a metaphorical sense though) He was in heaven.
Scriptural Support
Luk_3:22 And the Holy Ghost descended in a bodily shape like a dove upon him, and a voice came from heaven, which said, Thou art my beloved Son; in thee I am well pleased.
God the Father (voice from heaven) is in heaven and The Holy Spirit descends upon Jesus. Simple and straight forward. all other arguments are just metaphors for example
John 10:30 I and my Father are one.
While reading the Bible go to the clearest passages before going to the metaphoric ones. For example when studying the state of the dead do not start with the parable of Lazarus and the richman (please don't that's a parable you can find clearer statements which talk on that issue)
If you anyone does not agree here is a passage for you:
John 14:23 Jesus replied: If anyone loves me, they will obey me. Then my Father will love them, and we will come to them and live in them.
Obviously this is metaphoric because Jesus is in the Heavenly sanctuary now:
Heb 4:14 Seeing then that we have a great high priest, that is passed into the heavens, Jesus the Son of God, let us hold fast our profession
Heb 8:1 Now of the things which we have spoken this is the sum: We have such an high priest, who is set on the right hand of the throne of the Majesty in the heavens;
Heb 8:2 A minister of the sanctuary, and of the true tabernacle, which the Lord pitched, and not man.
When He finishes this ministry He will surely come again...
Rev 22:12 And, behold, I come quickly; and my reward is with me, to give every man according as his work shall be.
