Here "harmful spirit" may refer to either "a spirit that causes trouble" or "an evil spirit." See how you translated this in [1 Samuel 16:15](../16/14.md).
The phrase "rushed upon" means the harmful spirit influenced Saul. In this case it means it caused Saul to be troubled and act crazy. See how you translated a similar phrase in [1 Samuel 10:6](../10/05.md).