Did Moses kill an Egyptian

The answer to your question is found in the book of Exodus, chapter 2. The murder occured just before Moses left Egypt. At that time, Moses was being reared as the son of Pharaoh's daughter. Not much more is said of the account that I am aware of. If you are looking for information as to the time in terms of world history, it would have been around 1480 BC, since Moses spent 40 years as a shepherd and the Exodus occdurred in aound 1440 BC.