ANPIL? When it modifies a noun it becomes an adjective, and therefore is before it. When it modifies a verb, it becomes an adverb and goes at the end. e.g. Mwen anpil manje vs mwen manje anpil. How can I help students understand this?

You, pretty much, got it. 

But your given examples should be:

Mwen gen anpil manje (adj)
I have a lot of food.

Mwen manje anpil.(adv.)
I eat a lot.

manje is a verb and also a noun in Haitian Creole. So this example might be confusing to some students.
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As an adjective, anpil is placed before the noun.
Anpil (adj.) → many, a lot of, lots of, several, numerous, abundant, a great deal of



Examples:
Nou gen anpil konfyans nan ou.
We have a great deal of faith in you.

Mwen te ba li anpil lajan.
I gave him lots of money.

Anpil moun te panse li te mouri.
Many people thought he had died.

Gen anpil bagay ou pa'p ka konprann kounye a.
There are a lot of things you can't understand now.

Mwen te rele'l anpil fwa, e li pa't reponn.
I called her many times, and she didn't answer.


As an adverb, anpil modifies a verb or an attribute.

Mwen sonje w anpil. (modifies verb)
I miss you a lot.


Yo te fache anpil. (modifies attribute)
They were very angry.


Nou te mache anpil, anvan nou te rive. (modifies verb)
We walked a great deal before we arrived.

Mwen priye anpil jou sa yo.(modifies verb)
I pray a lot these days. 


Li te kontan anpil, lè li te wè w. (modifies attribute)
He was very happy when he saw you.

Mwen te panse anpil sou sa, e repons lan se "non". (modifies verb)

I thought a lot about it, and the answer is "no"

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