This is good stuff. Check out Lumen Gentium for more info. You can just google it and find it at the vatican website!
We talk about the Church comes from the unity of God and is a sign and instrument of that unity in the world. Therefore we call the church a "sacrament," a sign and instrument.
The church of Christ, both the invisible and the visible part, subsists (or exists or continues) in the Catholic Church, while some of her elements exist outside of her.
The Church is necessary for salvation, but you'll have to listen or read the text (paragraph 14-17) for all the nuances about other Christians and non-believers.
The part on the laity I think could be transformative people. Read it! Paragraphs 30--38