That hyphen is because "est-ce que" is a set phrase used for questions (while it literally translates to "is it that", it's usually best to simply use it to indicate a question and drop it when translating to English). The other hyphenation rule for questions is that when using the inverted form (verb-subject instead of subject verb), you add a hyphen between the verb and subject.
Hm. From what I've seen, that should be accepted. Just a tip, don't think of manger as a noun that's either singular or plural, just try to match the conjugations with their subject. Je mange, tu manges, il/elle/on mange, nous mangeons, vous mangez, ils/elles/ons mangent (pronounced the same as mange) EDIT: What do you eat is a correct translation, this comment is (mostly) for naught... whatevs.