The adverb "to eat" is "לאכול", while "אוכל" is the noun "food", or in that case it's the singular present form of the verb to eat.
So the conjugation of "to eat" make it lose its initial ל? It seems like the plural present forms also don't have ל.
Yes, "ל" is exactly like "to" in English.
You won't say "I am to eating" or "I to eat", and the same goes for Hebrew, it loses the "ל" and conjugated accordingly.
A/an is used for singular nouns and apples is plural so it would just be apples by itself
Because there is no definite article (ה). That changes everything. He is saying that he eats apples in general, not particular apples, which would be THE apples in English.
"To eat" is not an adverb; it is the infinitive form of the verb. An adverb is a word like "quickly" - a word which describes how fast you go, since "go" is a verb, and an adverb describes a verb. Another example (in English). He ate "slowly". In this example "slowly" is the adverb, but "ate" is the verb.