"I am eating an apple."
Translation:Mi manĝas pomon.
"-anta" is an adjective suffix, so the meaning of "mi estas manĝanta" would be closer to "I am someone who eats." than to "I am eating." Although It can be used to mean the latter, it is not used so much, to my knowledge.
But I could be wrong in assessing what is more common :-)
I am eating an apple =/= I am who is eating an apple. If you have a question about a verb, not about a person, you should use "mangxas", not "estas mangxanta"
No. "manĝanta" does not contain anything that means estas. It is just an adjective/participle and can be used only as such, and never as a verb! So it does need a verb (in this case, estas)
You could however combine it with estas and come up with "manĝantas" which then is, grammatically, a verb (but not commonly used).
(manĝas, not mangas). Both are "more neutral". Mi manĝas pomon - I eat an apple, Mi estas manĝanta pomon - I am who eats an apple.
Esperanto doesn't really distinguish simple present ("I eat") from present progressive ("I am eating"). I think the lessons are structured to make you think of those things more interchangeably.
If you wanted to precisely translate the present progressive, you could hypothetically say something like "mi estas manĝanta" or "mi manĝantas", but those sound weird and as far as I can tell they aren't really used.
In short, when speaking Esperanto, stick to the simple present.