What is the significance of the first "mi'Neged"?
Rashi: She sat, not opposite him, but at a distance, as the Pasuk continues.
Targum Yonasan: It hints at the fact that, when she saw that Yishmael was getting worse, she threw the image that she had begun worshipping far away, and began Davenning to Hashem. 1
As Rashi hints in the following Pasuk. In other words, she returned to Hashem, and it explains why Hashem answered their prayers.
Whyat is the translation of "ki'Metachavei Keshes"?
Rashi: Two bow-shots or 1 as far as one draws the bow.
How could she think that he will die? Hashem promised that he will be a great nation!
Hadar Zekenim: She had little faith. We find that she returned to the idolatry of her father's house.