Also in the skill I saw the sentence "Ears also need care" which was translated as "orelhas também precisam de cuidados". Why do we use the singular "cuidado" for this sentence, but "cuidados" in the other one?
Because it is a "locução adverbial" and always occurs as "com cuidado"
cheers Paulo :)
Is this the same as saying "The doctors treat the patients carefully"?
Yes. A more literal translation for "carefully" is "cuidadosamente".