I know from Acts 7 it is said that Moses knew he was a Hebrew prior to the burning bush event. What is your take on the possibilities that this was based on the Jewish tradition? Acts was written by Paul who was brought up a Pharisee and in the strictest Jewish tradition, could his writing be influenced by the traditions? I base my question on Exodus 4:10 where Moses said himself that he was slow of speech and tongue, yet in Acts, he was described as powerful in speech and action (Acts 7:22). To me, it would be safe to say that the Jewish tradition would have Moses "bigger than life." I'm not saying that I don't agree that Moses was a great servant of God, but it's man's nature to magnify people in history. Also that in Exodus 2:19, obviously Moses presented himself as an Egyptian. If he knew himself to be a Hebrew all his life wouldn't he have presented himself as a Hebrew when he went to visit the Hebrews in Pithom and Rameses?
Your question shows a belief that the Bible is a product of men and not of God. "But I make known to you, brethren, that the gospel which was preached by me is not according to man. For I neither received it from man, nor was I taught it, but it came through the revelation of Jesus Christ" (Galatians 1:11-12). Acts, by the way, was written by Luke, not Paul.
But to answer your question, Moses knew he was a Hebrew. He was raised as a child by his mother. "So the maiden went and called the child's mother. Then Pharaoh's daughter said to her, "Take this child away and nurse him for me, and I will give you your wages." So the woman took the child and nursed him" (Exodus 2:8-9). When he defended the Hebrew slave, note what is said at the end: "Now it came to pass in those days, when Moses was grown, that he went out to his brethren and looked at their burdens. And he saw an Egyptian beating a Hebrew, one of his brethren" (Exodus 2:11). That the daughters of Midian mistakenly thought Moses was an Egyptian in Exodus 2:19 (perhaps by his dress) does not indicate how Moses thought of himself.
There is no bigger than life presentation of Moses. The Bible presents both his good and bad qualities. He was slow of speech. But it doesn't mean that someone who needs time to think about what he says before he replies can't be powerful in his speech when he does open his mouth. What is recorded in Deuteronomy does show a man who used words powerfully. And his actions were powerful as well. But you should expect that of a man who had God telling him what to say and what to do. "So the LORD said to Moses: "See, I have made you as God to Pharaoh, and Aaron your brother shall be your prophet. You shall speak all that I command you. And Aaron your brother shall speak to Pharaoh to send the children of Israel out of his land" (Exodus 7:1-2). Stephen merely mentions that Moses had a reputation in Egypt as well prior to his fleeing the country.
Thank you for taking the time to answer my questions. I have one more question, the part about Moses' mother nursing him. I understand it as the mother weaned him and took him back to Pharaoh's daughter. That would put Moses at about the age of 1. At 1, even if he was taught that he was a Hebrew, how could he have remembered it?
What you are doing is applying modern assumptions to ancient cultures. The word for that is "anachronism." You assume that because today we try to have children weaned by the age of one, that this was always the practice. Even today weaning typically varies from four months to four years of age. See "A Natural Age of Weaning" by Katherine Dettwyler, Ph.D. Therefore, it isn't correct to assume that Moses was weaned by the age of one.
Nor does the Scriptures state exactly when Moses was returned to Pharaoh's daughter. "Then Pharaoh's daughter said to her, "Take this child away and nurse him for me, and I will give you your wages." So the woman took the child and nursed him. And the child grew, and she brought him to Pharaoh's daughter, and he became her son. So she called his name Moses, saying, 'Because I drew him out of the water'" (Exodus 2:9-10). That it was after he was weaned is clear, but how long after is not stated. Nor is there any implication that once he returned to Pharaoh's household that he stopped having interaction with his old nurse.
Therefore, any conflict that you see in this account is based on what you assume from what is not said. It isn't based on any hard evidence.