I suspect that many surnames came from vocations, like "Smith," or "Zuckerman" ("Sugar-Man" -probably a candy-maker).

That's only like a decade after the Ottoman empire was dissolved.

A change in surname is not necessary, just a transition from no surname to surname, which happened relatively recently in many places, or from explicit parentage descriptions ("X son of Y", etc.) to inherited family names.

Maybe. Often when families immigrated to America they tried to pick a spelling that would allow English speakers to pronounce their name close enough to what they were used to that they would understand they were being called. Sometimes the this was a different English word that had nothing to do with the meaning in the original language. (I suspect the same happens with immigrants elsewhere, but I know my family name is based on getting close to the original sound and that happens to be a word that has a different meaning in English)

I don't know if the original word was a occupation back in the old world or not. (the dialect my family spoke is no longer spoken so it would be difficult to research)

Pretty sure that if they're in English, it happened around the time William the Conqueror did the Domesday book, the first census of England.

Some are locations etc