Short answers, pulled from the story.
Battery is defined as the unlawful intentional infliction of harmful or offensive physical contact with another person without consent. American common law extends this to contact made by a substance set in motion by the aggressor, not only direct physical touching. The severity of the offense varies by jurisdiction.
Assault is the act of causing a person to apprehend that they are about to be subject to physical contact; battery is the actual unlawful contact itself. A person chasing and swinging at another commits assault, while the physical strike constitutes battery. Many jurisdictions, including New York, use the word assault to describe what common law calls battery, which leads to widespread public confusion.
Criminal battery in the United States is typically divided into simple battery, a misdemeanor at common law, and aggravated battery, which is a felony grade offense generally involving serious bodily injury or permanent disfigurement. In Florida, intentional infliction of great bodily harm is a second-degree felony, while battery that unintentionally causes great bodily harm is a third-degree felony. Sexual battery and family-violence battery are additional statutory categories in many states.
The question is legally unresolved. In DPP v Taylor and DPP v Little, a court held battery is a statutory offense under section 39 of the Criminal Justice Act 1988, but in Haystead v DPP the Divisional Court expressed the contrary opinion that battery remains a common law offense. Because no higher court has settled the matter, DPP v Little remains the preferred authority.
Recognized defenses include self-defense, defense of others, prevention of crime, mistake, duress, necessity, insanity, automatism, consent, medical procedure, sporting activities, and arrest by constable or citizen. Consent is not a valid defense when the battery results in actual bodily harm or greater.
Canada does not define battery in its Criminal Code; instead it uses assault and assault causing bodily harm. Scotland similarly has no distinct battery offense, treating such acts under its assault offense. Russia's Article 116 of the Criminal Code covers battery or similar violent actions causing pain, though it corresponds only loosely to the common law concept.