You have asked some interesting questions. I do not know of a Bible passage that clearly answers your questions, but I would like to point out what the Bible does clearly tell us. I believe that we can infer the answer to your question from these facts.
(1) God was gracious to warn Adam about sin and its consequences. God told Adam not to eat of the fruit of the forbidden tree. He told him that if he did, he would die (Genesis 2:15-17).
(2) When Adam sinned, God did not immediately put Adam to death, as his sin deserved. Instead, God sought Adam out, and exposed his sin (Genesis 3:8-13). God also indicated the consequences Adam and his wife would experience because of their sin (Genesis 3:8-19).
(3) God promised to provide a cure for sin and death (Genesis 3:15). He also provided Adam and Eve with coverings (3:21).
(4) God graciously removed Adam and Eve from the garden, and prevented them from returning to it. He kept them from eating of the tree of life, lest they live forever in their sin (3:22-24).
(5) God was gracious to turn the curse into the cure. Death kept Adam and Eve from living forever as condemned sinners. It was death (the death of Jesus Christ on the cross of Calvary) that ultimately and permanently defeated Satan, sin, and death -- because our Lord died in the sinner's place, and then rose from the dead. Even the woman's pain in childbearing was gracious, because it was through this painful process that the Messiah would someday come into the world to save sinners.
(6) God graciously gave Adam and Eve another son -- Seth -- after Cain killed Abel (4:25-26). It was after the birth of Seth that people began to worship the Lord (4:26). Did this include Adam? I am inclined to think so.
All of this suggests that Adam and Eve did seek God's forgiveness, and receive it. The Bible places the emphasis on Adam's sin (and not on his repentance and forgiveness) because it was through Adam's sin that all mankind was corrupted and brought under the same sentence of death (Romans 5:12-21). Adam turns our attention toward the sin of the human race. Jesus Christ turns our attention to life and righteousness.