1."Who & when did the author wrote the Book of Genesis?"
Author - Moses
Moses is the human author to the book of Genesis. 2 Kings 14:6 ascribe the book to Moses and Christ quotes passages of the law as from Moses in Matthew 19:8. This is what is called Mosaic authorship. But while Moses wrote the book of Genesis, this does not mean that He himself necessarily wrote every word. Jesus Christ was the author of the Sermon on the Mount, but he did not write it himself. What is meant by Mosaic authorship is that Moses was the fundamental or real author. In compiling it Moses may have used parts of already existing written documents. However under divine inspiration (2 Timothy 3:16; 2 Peter 1:20-21) Moses was lead by God the Holy Spirit to deliver to us 'the book of beginnings'.
Obviously he had to write it during his lifetime before giving it as described in the text.
Date Written - c. 1440 B.C.
The date of the Exodus can be arrived at from 1 Kings 6:1 and calculated at around 1446 to 1406 B.C. The Exodus preceded the time when Solomon began to build the temple (966 B.C.) by 480 years.
966 B.C. + 480 B.C. = 1446 B.C.
The date of the writing of the book of Genesis is difficult to determine with any certainty. The date given is only offered to indicate it's relative place in Bible history. This is likely the time when Moses would have written the first five books of the Old Testament.
2."Who & when did the author wrote the Book of Luke?"
Author - Luke
Traditionally the author of this book has been accepted as Luke the beloved physician and friend of Paul. (Colossians 4:14) He was probably the only Gentile author of the New Testament. He wrote both Acts and Luke which is the largest New Testament contribution of writings by any one author. Both Luke and Acts were written to the same person, Theophilus. The language and style of the two books are similar. While Luke is not mentioned as the author, Acts uses the personal pronoun 'we' in several places (Acts 16:10-17; 21:1-18; 27:1-28:16) in conjunction with the apostle Paul and by eliminating the unlikely candidates the most likely person is Luke Paul's friend. (Colossians 4:14)
Luke was not an original eyewitness or disciple of Jesus. He was a professional who researched his information and compiled his document under the inspiration of the Holy Spirit with special interest for the sick. It is thought that Luke was raised in Antioch in Syria but this is only speculation.
Also writen during his lifetime and after the events described in it.
Date Written - A.D. 63.
There seems to be more compelling evidence to place the date of Luke and Acts in the early 60's. The book of Acts ends with Paul still under house arrest and it would seem likely that if Luke knew of Paul release or death he would have mentioned it at the end of his book. For this reason it would seem appropriate to date his writings around A.D. 63.
A late date of around A.D. 70-80 has been suggested by some but Luke does not mention that the prophecy of the destruction of Jerusalem (Luke 21:20) was fulfilled and this seems to be his practice on other occasions. (Acts 11:28)
A late date does not seem probable. Luke probably wrote his works from Rome and sent to wherever Theophilus was living at the time.