Are all people saved by Christ just as all perished in Adam?
No, only those who are grafted into Him and receive all His benefits by a true faith.
Scripture references
What is true faith?
True faith is not only a certain knowledge by which I hold for truth all that God has revealed to us in His Word, but also an assured confidence which the Holy Spirit works by the gospel in my heart, that not only to others, but to me also, forgiveness of sin, everlasting righteousness and salvation are freely given by God, solely by grace, only for the sake of Christ's merits.
What then is necessary for a Christian to believe?
All things promised us in the gospel, which the articles of our universal and undoubted Christian faith briefly teach us.
Scripture references
What are these articles?
I believe in God the Father Almighty, Maker of heaven and earth.
I believe in Jesus Christ, His only begotten Son, our Lord; who was conceived by the Holy Spirit, born of the virgin Mary; suffered under Pontius Pilate, was crucified, died, and was buried; He descended into hell; the third day He rose again from the dead; He ascended into heaven, and sits at the right hand of God the Father Almighty; from there He shall come to judge the living and the dead.
I believe in the Holy Spirit; the holy catholic church, the communion of saints; the forgiveness of sins; the resurrection of the body; and the life everlasting. Amen.