What do adverbs modify and can it be ambiguous?

NB: Cutlery includes any hand implement used in preparing, serving, and especially [includes] eating food in Western culture.

especially qualifies "includes".

There are no rules in English - there is only guidance. Adverbs are quite flexible in their positioning but usually follow the verb. In any other position, they tend to give emphasis.

Especially refers to eating. (Cutlery is used in preparing food and serving it as well). In Western culture modifies the whole sentence.

Cutlery includes any hand implement used in preparing, serving, and especially eating food in Western culture. means

Cutlery includes any hand implement used in

• (1) preparing,
• (2) serving, and especially
• (3) eating ...

food, in Western culture.

This is deducible because 'preparing' and 'serving' don't stand sensibly on their own (without a complement). Serving in the trenches? At Wimbledon? So 'food[,] in Western culture' must be the common complement, omitted after the first two ing-forms.

A re-ordering is

Cutlery includes any hand implement used, in Western culture, in preparing, serving, and especially eating food.

......................

But you are right to suspect that an ambiguity could occur in such a sentence.

John enjoys cooking, eating, and especially catching fish. or just

John enjoys cooking, eating, and catching fish.

(the adverb placement is not the source of the ambiguity) is indeterminate: does John enjoy cooking fish, or cooking per se? Ditto eating. The ambiguity exists because of the listing, and the fact that cook[ing] and eat[ing] can be used with or without objects [complements].