In my dialect of English, "You eat the first apple" would be an imperative — a command (or suggestion, depending on mood), but "you are eating the first apple" would be a statement about what's happening. I doubt that the statement in French actually means the imperative, but I'm not certain. Anybody know?
The whole issue of "you eat" feels a little weird to native English speakers and much of that stems from the lack of a present continuous tense in French. So "tu manges" can be either "you eat" or "you are eating". In English, 99% of the time, "you" is not included in the imperative form. In French, "mange la pomme" is imperative and does not use "tu" either.
UK English speakers tend to use the present continuous to express the simple present. "You are eating my apple pie" would be usual without other context. But consider: "Every time you come here, you eat my apple pie!" That would be simple present (not imperative). You does not usually precede the verb in English (or French) imperative form, although it may do so for added emphasis or dramatic effect. "Eat my apple pie!" or, occasionally, "You - eat my apple pie!" although here we have a hiatus after the you which indicates an attention-getting vocative rather than a true imperative. I suppose one could say "You eat the first apple pie; I'll have the next one", though here I think you are not ordering someone to eat the first pie, but suggesting that they do so. Is it a real imperative? It seems to be more of a disguised question "(Why don't) you eat the first apple pie; I'll have the next one?"
Historically, the older imperative often required the pronoun ("Go ye, and sin no more".) Here we have one imperative with you (Go ye) and one without (sin).
No. You use the definite article whenever you would normally need a definite article, otherwise not. It's just another adjective. However, "first" is typically the kind of designation you give to something definite, so it's certainly more likely to come along with the definite article. However:
C'est une première édition. (It's a first edition.)
Je suis en première année. (I am a freshman.)
Ordinal numbers almost always come before the noun. http://french.about.com/od/grammar/a/numerical-adjectives.htm
Prime is stated as a valid option but is not correct. So how would you say you ate the prime apple. IE the most delicious apple conceivable of the batch of apples.