The Bible uses the word אָדָם ( 'adam ) in all of its senses: collectively ("mankind", 1:27), individually (a "man", 2:7), gender nonspecific ("man and woman", 5:1,2), and male (2:23-24). In Genesis 1:27 "adam" is used in the collective sense.
What mankind (adam) did as a whole is portrayed through individual Adam in Chapter 3 of Genesis. Mankind was enjoying perfect life in perfect system of things for an indefinite period. In character and qualities, they were all like gods and goddesses on earth. At some point in time they began to slip, developed loose-conduct, and became greedy with each one beginning to view the other with fleshly outlook (something symbolized by 'the sons of God seeing that the daughters of humans were beautiful, and marrying them ....' Fruit of the tree of good and bad, Satan, Eve ... are all symbols to suggest mankind experienced a fall.
Genesis writer did not follow a logical order. He was simply taking information from various sources (such as the Yahwist, the Elohist, the Deuteronomist and the Priestly) and putting it together. In other words, Genesis is all about history of mankind (not about an individual man named Adam) in two parts: pre-fall, and post-fall.
Not only the Genesis writer, even other Bible writers seldom show sense of propriety. For example, too many information about woman's menstruation, material contribution to tabernacle and later to temple, and discourse on "I am the bread of life" in John's Gospel, yet too little information about too important subject such as creation, make-up of man, proof about God's existence ...etc.