Further, Adam establishes the church?

Nope, by the Word of God and assigned to Adam
AELW1:104

"Therefore after the establishment of the church the government of the home is also assigned to Adam in Paradise. But the church was established first because God wants to show by this sign, as it were, that man was created for another purpose than the rest of the living beings. Because the church is established by the Word of God, it is certain that man was created for an immortal and spiritual life, to which he would have been carried off or translated without death after living in Eden and on the rest of the earth without inconvenience as long as he wished."