The men knew from studying the stars that the one who would become king had been born. They were trying to learn where he was. Alternate translation: "A baby who will become the king of the Jews has been born. Where is he?"
They probably believed that this star was the sign of a new king of Israel. Alternate translation: "the star that tells about him" or "the star that is associated with his birth"
"as it came up in the east" or "while we were in our country"
# worship
Possible meanings are 1) they intended to worship the baby as divine, or 2) they wanted to honor him as a human king. If your language has a word that includes both meanings, you should consider using it here.