La cita vs la fecha?
Apparently both of them mean "date", but what's the difference?
fecha is a date on the calendar. cita is a date you would go on, so like an appointment.
It depends on the country, but in Latin America we would use 'cita' when talking about a romantic encounter, for example: ''Tengo una cita con él'' - I have a date with him. (potential partner) And fecha is just on a calendar. :)
Wikipedia says that cita is a quotation. Is it also used that way in Latin America?
cita (or citación) can also be a quotation. citar can to make a date or to cite (quote) someone.
Yes, for example: ''citando al autor..'' (quoting the author...) -conjugation of the infinitive verb 'citar'- or ''la cita del libro..'' (the quote of the book..). But it's too formal I guess, we would use it in school.