The term "horn" was sometimes used to refer to a "flask" that was shaped like a horn and was used for holding water or oil. A flask of oil was used for anointing a king. See how you translated a similar phrase in [1 Samuel 16:1](../16/01.md).
The phrase "rushed on" means Yahweh's Spirit influenced David. In this case it means he enabled David to fulfill whatever Yahweh wanted him to do. See how you translated a similar phrase in [1 Samuel 10:6](../10/06.md).