Not true. As Dimitris says, the translation οf the Greek phrase should be "the ducks". But the way it's written it does not mean ducks in general. For a general meaning that should be "εσύ τρως πάπια", in singular just like in English. Alternatively, the plural would word, without an article: εσύ τρως πάπιες.
Because, here, it does not refeer to the animal, but to its meat. The same reason one would say "he eats beef". In English, the word "Meat" and words for kinds of meat are always singular, that is to say, they are not countable nouns and therefore they have no need for an article.
Τις (not της) is the definite article for feminine words in the accusative, in plural. Please check the declension tables in the tips and notes under Basics 1 (Tips and notes are available on the full/desktop website only). Της can also be a possessive (not in this sentence however), but it is in singular.