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She always behaves politely toward everyone.
Literal
She [topic-は] anyone [to-に][even-でも] always politely behaves.
誰にでも layers two universalizers: に (target) + でも ('even / any'). The result emphasizes 'to anyone at all, no matter who.' 礼儀正しく is the adverbial form of 礼儀正しい ('courteous, decorous'), an i-adjective compound from 礼儀 ('etiquette') + 正しい ('correct'). 振る舞う ('to behave / conduct oneself') is more deliberate than 行動する; it implies how one carries oneself, especially in social settings.