All three of your questions are briefly addressed in Pope Paul VI’s
Credo of the People of God, which says in part:
We believe that the Mass, celebrated by the priest representing the person of Christ by virtue of the power received through the sacrament of Order, and offered by him in the name of Christ and of the members of His Mystical Body, is indeed the sacrifice of Calvary rendered sacramentally present on our altars. We believe that, as the bread and wine consecrated by the Lord at the Last Supper were changed into His body and His blood which were soon to be offered for us on the Cross, likewise the bread and wine consecrated by the priest are changed into the body and blood of Christ enthroned gloriously in heaven; and we believe that the mysterious presence of the Lord, under the species which continue to appear to our senses as before, is a true, real and substantial presence (cf. n. 1526).
Thus, in this sacrament Christ cannot become present otherwise than by the change of the whole substance of bread into His body, and the change of the whole substance of wine into His blood, while only the properties of the bread and wine which our senses perceive remain unchanged. This mysterious change is fittingly and properly named by the Church transubstantiation. Every theological explanation which seeks some understanding of this mystery must, in order to be in accord with Catholic faith, maintain firmly that in the order of reality itself, independently of our mind, the bread and wine have ceased to exist after the consecration, so that it is the adorable body and blood of the Lord Jesus which from then on are really before us under the sacramental species of bread and wine (cf. nn. 1519, 1527, 1577), as the Lord willed it, in order to give Himself to us as food and to bind us together in the unity of His Mystical Body.
The unique and indivisible existence of the Lord glorious in heaven is not multiplied, but is rendered present by the sacrament in the many places on earth where the eucharistic sacrifice is celebrated. And this existence remains present, after the celebration of the sacrifice, in the Blessed Sacrament which is in the tabernacle as the living heart of our churches. Therefore, it is our sweet duty to honour and adore, in the Blessed Host which our eyes see, the Incarnate Word Himself whom they cannot see and who, yet, without leaving heaven, is made present before us.