Pope Paul VI addressed this quite succintly in his encyclical Ut unum sint
The unity of all divided humanity is the will of God. For this reason he sent his Son, so that by dying and rising for us he might bestow on us the Spirit of love. On the eve of his sacrifice on the Cross, Jesus himself prayed to the Father for his disciples and for all those who believe in him, that they might be one, a living communion. This is the basis not only of the duty, but also of the responsibility before God and his plan, which falls to those who through Baptism become members of the Body of Christ, a Body in which the fullness of reconciliation and communion must be made present. How is it possible to remain divided, if we have been "buried" through Baptism in the Lord's death, in the very act by which God, through the death of his Son, has broken down the walls of division? Division "openly contradicts the will of Christ, provides a stumbling block to the world, and inflicts damage on the most holy cause of proclaiming the Good News to every creature".
(1) Am I right in thinking that all the Catholic Churches who are in communion with the Bishop of Rome (and this would include Melchites, Maronites, Byzantine Catholics, etc.) are under one "jurisdiction"?
(2)If the above is true, are they all under the same Canon Law?
(I vaguely remember hearing that this was somewhat controversial.)
(3)Do we all use the same Catechism?
(Again, I vaguely recall that, while nobody in the Eastern Catholic Churches would reject anything in the Catechism as an error, nevertheless there are some difficulties because of terminology, style, emphasis.)