What can we learn about the family from The Bible, in Genesis 1-3 ?
In the Bible, in Genesis, there are several key things that we can learn about the family. The first is that God, upon placing Adam and Even in the garden itself, commanded them to have a family. Having a family was one of the first commands given by God to people here on earth. They were commanded to "multiply and replenish the earth." So, family was important enough to God for Him to make it a top priority in His commandments.
Another thing that we can learn is the importance of marriage in the role of the family, and in the husband and wife being, as much as they can, of one heart and one mind. At the end of Genesis chapter 2, the pattern of a woman and a man coming together as husband and wife, away from their own mothers and families, is established. Adam states that they, as a couple, should "be one," hinting at the importance of unity in a marriage. After they have partaken of the fruit, God states that the woman shall then produce children, and that Adam shall work to take care of them. This establishes rather traditional roles of the family, with the wife as the caretaker of the children, and the husband as the breadwinner. God mentions that the husband shall "rule over" Eve, which many people have misinterpreted as exerting repressive power over women, and used as an excuse for abuse, but really just refers to his role as a leader for his children and provider for the family as a whole.
If you look closely at the establishment of the first commandments and family in Genesis 1-3, some very interesting facets of the family can be learned. I hope that my thoughts helped a bit; good luck!