A - Thanks for the question. Does the Church teach that outside the Church there is no salvation? Yes. But, we have to understand what this means in context. Think of it this way. There is no salvation apart from Jesus. Jesus established His Body and Bride, The Church, as the instrument of that salvation. Therefore, there is no salvation outside of this instrument of his salvation - outside of Christ's Body/Bride. So, who belongs to this Church and how?
The Catechism teaches:
Who belongs to the Catholic Church?
836 "All men are called to this catholic unity of the People of God.... And to it, in different ways, belong or are ordered: the Catholic faithful, others who believe in Christ, and finally all mankind, called by God's grace to salvation."837 "Fully incorporated into the society of the Church are those who, possessing the Spirit of Christ, accept all the means of salvation given to the Church together with her entire organization, and who - by the bonds constituted by the profession of faith, the sacraments, ecclesiastical government, and communion - are joined in the visible structure of the Church of Christ, who rules her through the Supreme Pontiff and the bishops. Even though incorporated into the Church, one who does not however persevere in charity is not saved. He remains indeed in the bosom of the Church, but 'in body' not 'in heart.'"
838 "The Church knows that she is joined in many ways to the baptized who are honored by the name of Christian, but do not profess the Catholic faith in its entirety or have not preserved unity or communion under the successor of Peter." Those "who believe in Christ and have been properly baptized are put in a certain, although imperfect, communion with the Catholic Church." With the Orthodox Churches, this communion is so profound "that it lacks little to attain the fullness that would permit a common celebration of the Lord's Eucharist."
What about non-Christians? Can they be saved?
843 The Catholic Church recognizes in other religions that search, among shadows and images, for the God who is unknown yet near since he gives life and breath and all things and wants all men to be saved. Thus, the Church considers all goodness and truth found in these religions as "a preparation for the Gospel and given by him who enlightens all men that they may at length have life."From this, we can understand the following better:
846 How are we to understand this affirmation, often repeated by the Church Fathers? Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body:Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.847 This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church:
Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience - those too may achieve eternal salvation.848 "Although in ways known to himself God can lead those who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men."
I hope this helps explain better these questions. Peace.