"He eats the dinner."
Translation:Mangia la cena.
"Mangia" can indeed mean "he eats" or "she eats", but "they eat" would be "mangiano".
There is likely to be clarifying context in a regular conversation, or you could always just ask the person you're talking to. After all, "he eats" is also ambiguous. Which "he"?
Not sure which article you're referring to, though.
It could also be the imperative, yes, but this early in the tree it's safe to assume it's all declarative. Italian allows the subject pronoun to be omitted much of the time.
That sounds very odd. In the simple present tense, there is an important difference between the first person and third person form. I can't imagine why it would do that aside from a glitch.
Now, if it were the second person, then the formal of that looks like the third person, but Duo doesn't really teach that detail.