How do Christians coexist as Monotheists & yet pray to Father, God as Son & God as Spirit?
God is One.
God is expressed as three Persons in the New Testament (Bible).
All analogies & metaphors will be in danger of over-explaining, or misrepresenting.
Think of the Virgin Mary, when before she had married Joseph the Carpenter of Bethlehem, saw:
1.Gabriel, an Archangel, who told her she would bear the expected Messiah (CHRIST in Greek, meaning the Anointed One). Anyone who has been a born-again Christian (Baptist, Presbyterian, Pentecostals ... ) even for a year, will figure anointing means "power of the Spirit of God."
2. Mary had to give her permission for the Holy Spirit to come upon her for Jesus to be fully human & live the womb-to-tomb experience. Mary gave her permission when she heard the "Seed" would be in the line of King David, the "Hope" of Israel. She sang the most beautiful Song, the Magnificat, which is the first words: "My soul magnifies the LORD" (YHWH: YaHWeH) who has given me this honor among women, to bear the Hope of Israel. The Holy Spirit never forces Himself (Person, remember) upon anyone. If you wish to experience the reality of God's Spirit, you must invite Him ("Holy Spirit of God, please help me know Jesus").
3. God claims Jesus as His Beloved Son; that is true and borne out in Scripture as in Mark 1: 11; Matthew 3: 17; Luke 3: 22; 2 Peter 1: 17).
The Spirit is the One who "overshadowed Mary" the virgin, and prevented the father of Jesus on earth, becoming Joseph. It may be correct to see no difference between God the Father, and God the Holy Spirit, as the One Father of Jesus. Difficult to say in any language, but God has never been expressed fully in any human language ... even human love defies words!
4. Western Christianity has created a problem, with its black and white thinking styles. The three Persons (with distinct personalities) in the Godhead are NEVER in competition. The Father speaks well of the Son (Jesus) and Jesus speaks well of Abba-Father and Holy Spirit (Ruach haKodesh), and the Holy Spirit teaches nothing about Himself, but brings to remembrance all that Jesus spoke on earth (as Jesus told His disciples in John 14, before He was crucified).