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I think the first part of your post was about the LG references.
(LG 7) By communicating His Spirit, Christ made His brothers, called together from all nations, mystically the components of His own Body.... In that Body the life of Christ is poured into the believers who, through the sacraments, are united in a hidden and real way to Christ who suffered and was glorified.
(n. 7) All the members ought to be molded in the likeness of Him, until Christ be formed in them.(62) For this reason we, who have been made to conform with Him, who have died with Him and risen with Him, are taken up into the mysteries of His life, until we will reign together with Him.(63) On earth, still as pilgrims in a strange land, tracing in trial and in oppression the paths He trod, we are made one with His sufferings like the body is one with the Head, suffering with Him, that with Him we may be glorified.(64)
(n. 8) This is the one Church of Christ which in the Creed is professed as one, holy, catholic and apostolic, (12*) which our Saviour, after His Resurrection, commissioned Peter to shepherd,(74) and him and the other apostles to extend and direct with authority,(75) which He erected for all ages as "the pillar and mainstay of the truth". This Church constituted and organized in the world as a society, subsists in the Catholic Church, which is governed by the successor of Peter and by the Bishops in communion with him,(13*) although many elements of sanctification and of truth are found outside of its visible structure. These elements, as gifts belonging to the Church of Christ, are forces impelling toward catholic unity.
(LG 9) For those who believe in Christ, who are reborn not from a perishable but from an imperishable seed through the word of the living God,(88) not from the flesh but from water and the Holy Spirit,(89) are finally established as "a chosen race, a royal priesthood, a holy nation, a purchased people . . . who in times past were not a people, but are now the people of God".(90) ... That messianic people has Christ for its head, "Who was delivered up for our sins, and rose again for our justification",(91) and now, having won a name which is above all names, reigns in glory in heaven. The state of this people is that of the dignity and freedom of the sons of God, in whose hearts the Holy Spirit dwells as in His temple. Its law is the new commandment to love as Christ loved us.(92) Its end is the kingdom of God, which has been begun by God Himself on earth, and which is to be further extended until it is brought to perfection by Him at the end of time, when Christ, our life,(93) shall appear, and "creation itself will be delivered from its slavery to corruption into the freedom of the glory of the sons of God".(94) So it is that that messianic people, although it does not actually include all men, and at times may look like a small flock, is nonetheless a lasting and sure seed of unity, hope and salvation for the whole human race. Established by Christ as a communion of life, charity and truth, it is also used by Him as an instrument for the redemption of all, and is sent forth into the whole world as the light of the world and the salt of the earth.(95)
EDIT: Isn't it irritating how easy it is to get confused between the "Post" and "Previous Post" text boxes, especially when you're trying to comment inline?