Well, keep in mind that SC is primarily about the revision of the totality of the liturgy (Mass, Sacraments, Sacramentals, Divine Office, Calendar, Sacred Music, Sacred Art,), and not a doctrinal exposition of the Liturgy and its parts. In that sense, it is more akin to the reform decrees of Trent concerning the Liturgy, than it is to the doctrinal decrees. The Constitution necessarily assumes that "the dogmatic principles which were laid down by the Council of Trent [remain] intact" (Para. 55). So there is no need to repeat everything Trent said, because that is not the point of the document. The following is adequate to address your concerns:
12. We learn from the same Apostle that we must always bear about in our body the dying of Jesus, so that the life also of Jesus may be made manifest in our bodily frame (31). This is why we ask the Lord in the sacrifice of the Mass that, "receiving the offering of the spiritual victim," he may fashion us for himself "as an eternal gift" (32).47. At the Last Supper, on the night when He was betrayed, our Saviour instituted the eucharistic sacrifice of His Body and Blood. He did this in order to perpetuate the sacrifice of the Cross throughout the centuries until He should come again, and so to entrust to His beloved spouse, the Church, a memorial of His death and resurrection: a sacrament of love, a sign of unity, a bond of charity (36), a paschal banquet in which Christ is eaten, the mind is filled with grace, and a pledge of future glory is given to us (37).
48. Christ's faithful ... should be instructed by God's word and be nourished at the table of the Lord's body; they should give thanks to God; by offering the Immaculate Victim, not only through the hands of the priest, but also with him, they should learn also to offer themselves; through Christ the Mediator (38), they should be drawn day by day into ever more perfect union with God and with each other, so that finally God may be all in all.
Forgot to add: I know that the Council Fathers never use the word "transubstantiation," so precisely what they mean by "the body and blood of Christ" is open to interpretation.
This seems clear enough:
7. He is present in the sacrifice of the Mass, not only in the person of His minister, "the same now offering, through the ministry of priests, who formerly offered himself on the cross" (20), but especially under the eucharistic species.
Exactly.