Hi, from a real cop, here's some bits and bobs:
Section 5 public order is basically a catch all offence used when someone is being a general pratt in public
For domestic violence, we do a range of paperwork; there's DVPNs, DVPOs, PPNs, VRAs and all sorts. These are all googleable
Section 47 assault is a common one; it's stuff that causes bodily harm but isn't going to drastically affect's the victims life, such as knocking a tooth out or splitting someone's lip
Section 39 is your common assault for stuff like shoves and punches that don't land well, as well as slaps etc.
You can racially aggravate any offence, which carries a compulsory sentence increase... which I have forgotten the specifics of!
PM me if you want to know anything.