What does this mean, "Thus, in baptism, we receive the Holy Spirit and in chrismation we are made "Christs", anointed to be children of the Father"?
What happens when we are baptized? We are joined to the Church of Christ. The Church of Christ is the mystical body of Christ, with Christ as the head. When Christ was baptized by the Forerunner, the Holy Spirit descended and "rested" in Christ. In doing so, Christ made the Holy Spirit "rest" in all of humanity as it rested eternally in Him before the incarnation. When the Father said "this is My beloved Son, in whom I am well pleased," this extends to all of humanity, where St. Paul teaches as the "adoption." Thus by the Holy Spirit we are made "children" to the Father by adoption, that we may cry out to Him "Abba Father" as the Son eternally had.
Finally we are anointed with the chrism. The word "Christ" comes from the word that mean "anointed." We are made "christs", literally anointed. And this means that we are ALL "kings and priests" because of this anointing, or "christening". We are made "saints." By having this anointed authority, we are able to partake of the Eucharist.
You cannot have salvation without these.