"You should eat at least an apple a day."
Translation:Εσύ πρέπει να τρως τουλάχιστον ένα μήλο την ημέρα.
In my mind, will have to is a better translation to θα πρέπει να, just for the future element to be a bit more visible. No? ^.^
να φας would be good for a one-time action, but here, you are commanding a repeated action (every day), so να τρως is the appropriate verb form.
It is. Both words mean the same thing. It's just that, sometimes, when the previous word ends in a vowel like η or α, μέρα is preferred, so that the two vowels (η/α and the η in ημέρα) don't clash.
It's the same story for ημέρα. When the previous word ends in a consonant (usually ν), it sounds a bit more neat to use ημέρα than μέρα. ^.^
τη μέρα and την ημέρα are exactly the same thing, and since it follows the rules you can