If God is a Trinity, are Father and Son manifestations of Divinity without being spirits? If God is a Trinity of Father, Son, and Holy Spirit, does this mean that Father and Son are manifestations of Divinity without being spirits, so that only the Holy Spirit is a spirit?

Please answer according to the Catholic Church.
Both God the Father and the Holy Spirit are spirits. 

For example, catholic.com states,


  ... verses, such as John 4:24, where Jesus teaches us: "God is spirit, and those who worship him must worship in spirit and truth." This means God has no body, because a spirit is, by nature, an incorporeal being. 
  
  The Church Fathers, of course, agreed, and loudly declared the fact that God is an unchangeable, immaterial spirit who has an entirely simple ("incomposite") nature
  
  It is true that Jesus, who is God, assumed an earthly body when he was born of the Blessed Virgin, and that this body, now glorified, continues to exist. But since the Lord only took on human flesh in these "last days," and since God has always existed, without beginning or end, we must still conclude that having a body is not part of God’s unchangeable nature: he exists in eternity as pure spirit, even though he chose for the Son to also take on a human nature in addition to his bodiless, timeless, divine nature.


Source: http://www.catholic.com/tracts/god-has-no-body

God the Son existed as a spirit before his incarnation as Jesus of Nazareth.

And, to be exact, none of the persons of the Trinity are "manifestations of God"; each person of the Trinity is God.