The New Testament shows that Christ deliberately created his Church to be the vehicle of his continuing mission in the world. He promised to remain present in his Church for all time, and he lovingly guides it through the presence of the Holy Spirit.
To ensure the success of this mission, Christ gave his Church the ability to teach, govern and sanctify with Christ’s own authority. The Apostles appointed successors to ensure that the Gospel would continue to be handed on faithfully as “the lasting source of all life for the Church” (Vatican II, “Lumen Gentium” 20; also Catechism #860).
The source and guarantee of this Church authority is Christ’s continuing presence in his Church — “Lo, I am with you always, to the close of the age” (Mt 28:20).
The purpose of this authority is to give the Church the ability to teach without error about the essentials of salvation: “On this rock, I will build My Church, and the powers of death shall not prevail against it” (Mt 16:18).
The scope of this authority concerns the official teachings of the Church on matters of faith, morals, and worship (liturgy & sacraments). We believe that, because of Christ’s continued presence and guarantee, his Church cannot lead people astray with its official teachings (which are distinct from the individual failings and opinions of its members, priests, bishops, and Popes).
I fully agree with your first 3 statements, as the Bible materially provides for such, and see them being fulfilled in the world today by the church universal that (at the least) preaches the apostolic gospel that convicts souls of their utter inability to escape Hell or gain Heaven by the merit of their works, but who repent of such and their old life of sin to trust in the Biblical Christ and His sinless shed blood for salvation (Acts 20:21; 26:20; Rm. 3:9-5-1; Eph. 2:8, 9; 2 Tim. 1:9). And upon which they are spiritually added to the church (1 Cor. 12:13).
As for 4 and 5, this is an unwarranted extrapolation out of Mt. 16:18, in ascribing infallibility to an autocratic church that essentially holds that according to her interpretation, implicit trust is warranted, and you need not do as the Bereans did (Acts 17:11), and must not allow that she can be wrong in her interpretation of what she deems essential doctrine (which itself is an essential doctrine). Meanwhile, very little of the Bible has been infallibly defined (as well as an infallible list of infallible teachings, which allows much uncertainty.
I do believe God will ensure that the Biblical substantiated gospel and it essentials will be preached by His true churches, and that God will preserved by His church, which is always a relative remnant, even if it’s leaders err in essentials. In such a case, like as in Israel of old, God raises up prophet type persons who can reprove error, and call them to repentance. Men such as Huss, Tyndale, Luther, Whitefield, Spurgeon, Wesley, were some of them, and by such the declension and aberrations of Christian faith was much arrested and revival brought, to the salvation of billions since. We now are in the age of increasing declension, with the contrast being increasingly clear as to who bow to Baal versus Christ.