It's sort of self-explanatory dont you think? An assault is an unlawful touching or strking and it resulted in physical injury to the person who was struck.
It covers bodily injury. I am a little confused with your question... It covers injuries to others if you are held or considered at fault for their injuries ex. you are held at fault in an auto acc.
I personally carry 100k/300k meaning the limit that can be paid per accident for an injury that I cause is 100k per person and 300k per accident. You will need to decide what you are comfortable...