"Do they cook well?"
Translation:Они хорошо готовят?
"хорошо" describes the verb, so it is an adverb. Adverbs typically come before the verb. Another example: Ты много читаешь?"
My wife, a native Russian, says it only depends on the pronunciation. Both word orders should be correct...
so to a Russian person, They well cook?, is understood the same as an English speaking person understanding Do they cook well?