Caveat: this is a difficult sentence in general and there is no settled translation.

However it's translated, it's easy to make a subtle assumption about the text that isn't actually there (although a straightforward inference coming from a trinitarian position).

In the article Philippians 2:6-8 the authors conclude

"The verse is not speaking either of Christ’s giving up his “Godhood” at his incarnation or of his God-nature being willing to “hide” so that his man-nature can show itself clearly. Rather, it is saying something else. Scripture says Christ was the “image of God” (2 Cor. 4:4), and Jesus himself testified that if one had seen him, he had seen the Father. Saying that Christ was in the “form” (outward appearance) of God is simply stating that truth in another way. Unlike Adam, who grasped at being like God (Gen. 3:5), Christ, the Last Adam, “emptied himself” of all his reputation and the things due him as the true child of the King. He lived in the same fashion as other men. He humbled himself to the Word and will of God. He lived by “It is written” and the commands of his Father. He did not “toot his own horn,” but instead called himself “the son of man,” which, in the Aramaic language he spoke, meant “a man.” He trusted God and became obedient, even to a horrible and shameful death on a cross."

So it's not that there was time 1 'he empties himself' time 2 'he is born'.

To answer the questions

1. He emptied himself, starting with his birth, of all his reputation and the things due him as the true child of the King. He lived in the same fashion as other men.

2. "How can one empty oneself by birth[?]" The text doesn't quite say this, and the Biblical Unitarians in the article quoted above would say it's a misreading of the text. The emptying doesn't happen before, but starting with his birth.

Caveat: this is a difficult sentence in general and there is no settled translation.

However it's translated, it's easy to make a subtle assumption about the text that isn't actually there (although a straightforward inference coming from a trinitarian position).

In the article Philippians 2:6-8 the authors conclude

"The verse is not speaking either of Christ’s giving up his “Godhood” at his incarnation or of his God-nature being willing to “hide” so that his man-nature can show itself clearly. Rather, it is saying something else. Scripture says Christ was the “image of God” (2 Cor. 4:4), and Jesus himself testified that if one had seen him, he had seen the Father. Saying that Christ was in the “form” (outward appearance) of God is simply stating that truth in another way. Unlike Adam, who grasped at being like God (Gen. 3:5), Christ, the Last Adam, “emptied himself” of all his reputation and the things due him as the true child of the King. He lived in the same fashion as other men. He humbled himself to the Word and will of God. He lived by “It is written” and the commands of his Father. He did not “toot his own horn,” but instead called himself “the son of man,” which, in the Aramaic language he spoke, meant “a man.” He trusted God and became obedient, even to a horrible and shameful death on a cross."

So it's not that there was time 1 'he empties himself' time 2 'he is born'.

To answer the questions

1. He emptied himself of all his reputation and the things due him as the true child of the King. He lived in the same fashion as other men.

2. "How can one empty oneself by birth[?]" The text doesn't quite say this, and Young's literal translation reads "but did empty himself, the form of a servant having taken, in the likeness of men having been made". So the Biblical Unitarians in the article quoted above would say it's a misreading of the text. The emptying doesn't happen before, or really even starting with his birth, but at some point in his life (presumably with a gradual increasing awareness as he grew up that he was the Messiah), most notably dying on the cross.