No. The Hebrew word for covenant is "shiva" which is also the number seven. Seven is a sign of covenant. When one makes an oath, in Hebrew, he is said to have "sevened" himself. It's not numerology, it's a recognition of God's Grace at work through successive covenants.
Sorry, but God doesn't make mistakes.
I didn't say God made a mistake... Adam did. He and his heirs paid the price. To say that God intended man to fail as part of His plan from the beginning is to fail to understand free will and to put one's faith in predestination.
God devised another plan, and that nearly was goofed up except for Noah.
No. God's salvation for man was begun with the protoevangelium. The line of Seth was set apart for God. When they intermarried with the other lines, God acted to preserve His promise in Noah. Man is still the one making mistakes.
The biggest mistake occurs with the children of Israel in the desert. They were intended to be a priest-nation to go out to the world and make disciples of the nations. However, they returned to their idols and broke the covenant while Moses was on the mountain. God gave them correction and removed the priestly role from the nation to the tribe of Levi. Then when they failed to enter Canaan at God's command for fear of the inhabitants, God put them to wandering until that wicked generation was gone.
The next generation failed even greater than their parents at Baal-peor and then the second law (Deuteronomy) was given by Moses (instead of by God as was the law of the covenant).
Through it all, God was faithful to His promise and carried out His perfect plan in spite of imperfect people.
But God did intend for man to fall. He knew very well what would happen and He allowed it. That is an inescapable truth. It isn't a matter of putting one's faith in predestination. It is a matter of acknowledging that God deliberately allowed Satan in the garden, was not around knowing that Adam and Eve would succumb to temptation, allowed man to sin and then announced His curse on all mankind. God not only knew all of this would happen before the foundations of the world but He designed it this way.