Nicknames that stuck

Yes, many nickname surnames were handed out ironically, calling a tall man Short or a heavy man Little. Villagers used sarcasm as often as literal description, and once a joke name passed to a person's children, it became a fixed, hereditary surname regardless of its accuracy.

No, not the way they once did. Medieval bynames turned into surnames because communities kept inventing new names and handing them to children informally. Once countries required fixed, registered hereditary surnames, that open-ended process stopped, even though people still pick up nicknames every day.

Not always. Some surnames that look like nickname surnames actually started as something else entirely, since a descriptive-looking name can be a coincidence. Broadhead reads like a nickname for someone's head shape, but in several family lines it traces back to a village name instead.

Not necessarily. Descriptive surnames like White, Swift, or Young were common enough that unrelated families across different regions ended up with the identical name, since any number of villages could independently nickname a pale man, a fast runner, or a young-looking man the same way.