Could the "man" created in Genesis 1:27 be something different than the offspring produced from Adam and Eve?
In Genesis 1:27 it is stated that God created “man”, with gender male and female. In Genesis 2:5-7 it is stated that God formed a man and called him Adam. Does this mean that God has created “man” first then later God formed Adam and Eve? In Genesis 6:1-2 it is stated that in the world there are two categories of people: Men and Sons of God. Does this mean that men came from “man” and the Sons of God is came from Adam? If all people in the world are descended from Adam, does this mean that God approves of “incest” marriage.
Genesis chapter 1 describes the creation of the universe and of the earth. It also describes how land appeared out of the water, after which life appeared in the water, then on the land, with ever-more-complex life forms. Last of all, God created man. A lot happens in Genesis chapter one! The use of the word “man” here is generic. It means that God created humanity. Presumably, “man” here means men and women.
Genesis 2:4-25 is an expansion on part of what happened on the sixth “day” of creation. It describes one of the things which happened on the sixth “day”–the creation of human beings–in quite a bit more detail. The additional detail we find in Genesis 2 is that God created a male human being first, followed by a female human being. So, the answer to your question is that when it says God formed “man” in Genesis 1:27 and that he formed a man, then a woman in Genesis 2:5-7, these are consistent. The second description is simply giving more detail concerning what was described in brief in Genesis 1. As for Genesis 6:1-2, the meaning of this passage is obscure. Scholars and inquisitive sincere Christians have reached a range of conclusions on this passage. Possibly it is simply saying that the sons of God (ie male people) had sexual relations with the daughters of men (ie female people) and produced offspring. This would not be a surprising statement! Another interpretation is that some sort of angelic beings had sexual relationship with human females, giving birth to offspring which may not have been exactly the same as the normal offspring of human men and women. The book 1st Enoch gives an interpretation along these lines. Since we cannot be absolutely sure which of these interpretations is correct, we may have to settle for not being sure. Obviously, there is no essential question of doctrine or theology at stake here, so we do not have to be all that concerned about some ambiguity on this passage.
I am pretty sure that Genesis 6:1-2 does not mean that “men” can from “man” and that, separately, the Sons of God came from Adam and Eve. To be honest, I cannot see how you would even come up with this idea from the passages. According to the Genesis creation account, “men” came from Adam and Eve. Who the “Sons of God” are in this passage is problematic, but in any case, I do not see how your proposed interpretation can work. Perhaps I am misunderstanding you, and you should write to me again to clarify, but that is my response to what you have asked.
If all humans literally came from Adam, then, yes, fairly close relatives did marry and produce children. Incest was listed as a sin in the covenant of Moses, but this may have been because it is dangerous, as it tends to produce genetically unhealthy offspring. It may not be because incest is inherently sinful, but for health reasons. Perhaps the earliest humans were not as genetically deficient and having children by closer relatives would not have been as unhealthy. I am not sure. Adam and Eve may have had dozens of children, each of which may have had dozens of children, so within a very short time, incest would not have been required for marriage. We may have to settle for not being sure on this one.