It depends on the subject of the sentence. If you can speak English, you can think of this "se" as a kind of passive (in Spanish they're called "pasiva refleja"). In the sentence "se organiza una fiesta", "una fiesta" is the subject, so the verb must be in 3d person singular. If it were "se organizan fiestas", the subject would be plural (and the verb too).

"los presentes" is similar to " the people who attend". Im this case the people who attend the fair Las festividades que se organiza en su honor (incorrect) Las festividades que se organizan en su honor (correct) También se organizan una feria (incorrect) También se organiza una feria (correct)

Las personas que asisten a un evento. A synonym: "Los participantes"

"También se organiza (singular) una feria (singular) donde los presentes (people attending) pueden comprar recuerdos de su patrono y otras artesanías." "Las festividades (PLURAL) que se organiza (SINGULAR) en su honor..." THAT'S WRONG "También se organizan (PLURAL) una feria (SINGULAR)" THAT'S WRONG.