"Does he eat?"
There is no "mange-il"- what you're looking for is mange-t-il. The same inversion rule goes for elle (mange-t-elle). The t doesn't mean anything, but it's there for fluidity purposes.
two exact solutions are presented in the multiple choice, but only one of them is reported as correct.
That's the infinitive form of the verb. You need to conjugate it for the 3rd person singular form because "he" (a man) is eating.
In 'est-ce qu'il mange', the qu' is the shortened 'que' meaning 'that' (in an auxiliary sense, like when you would say 'I had gone'), so 'est-ce qu'il mange literally translates to, "Is it that he eats?" (simplified to 'does he eat') If you put 'Qu'est-ce qu'il mange' instead, it would mean "what (does he eat/is he eating)". Or you could write, Il mange quoi ? if you wanted to sound incredulous, like, " Tu manges quoi ? Les papillones sont répugnants"