Thats 2 offenses. Remember also that the VWP question relates to arrests.
You basically need to know the District of Columbia criminal codes, and whether the maximum possible sentence is greater than 5 years in US jail - not the maximum possible under UK law. Also whether the assault charge could be classed as a crime involving moral turpitude.
Basically the time line is not good, as a visa wouldn't be issued before the court hearing.
Immigration lawyer may be your best bet on this.