Is the sign of the Cross as well as the crucifix a Catholic “trade mark”?

Why do Catholics have crucifix in their home and Churches; priest, bishops, cardinals, popes and the faithful wear crucifix in their neck and make a sign of the cross before and after prayer and always say “In the name of the Father, and of the Son and of the Holy Ghost, amen”. Would this mean that the culmination of the Catholic Faith of salvation was on Christ death and His triumph over death in order for a man’s death to sin will be brought back to immortal life in unity to Christ? If this is so, the sign of the cross will forever in history and the age to come to be remembered and not forgotten in our hearts. Are there theological, history, catechism, canon on this?