Emma rescues the Mayor from a fire and the Sheriff's debate takes place in episode 1x08 "Desperate Souls". From episode 1x11 "Fruit of the Poisonous Tree". From episode 1x14 "Dreamy". Appears in 2 more episodes.
From episode 7x05 "Shut Up, Dr. Phil".
Source: Laina Weber
Sheriff Velchik talks to the townspeople in episode 2x12 "Johari Window".