Learn Dutch: De champagne laat zich perfect combineren met de oester. - The champagne can be perfectly combined with the oyster.

This is the passive potentiality construction you are learning in this lesson. Literally, it translates to 'lets itself combine'. Using zich laten plus a bare infinitive is a very common and elegant way in Dutch to say that something is able to have an action done to it.

Could I use kunnen and a normal passive construction instead, like kan perfect gecombineerd worden?

Yes, that is grammatically correct and means the exact same thing. However, laat zich combineren is highly idiomatic and sounds much more sophisticated. You will frequently see this construction in food reviews, formal writing, and marketing language.

Why is the singular de oester used here instead of the plural oesters?

Just like in English fine-dining or wine-tasting descriptions, Dutch often uses the singular definite noun to refer to a category of food as a whole culinary concept. Saying met oesters is also completely fine, but met de oester fits the elegant, descriptive tone of this sentence much better.

What dictates the position of the adverb perfect in this sentence?

In a main clause, the conjugated verb (laat) and the infinitive (combineren) form a 'verb bracket' that holds the rest of the sentence. Because the reflexive pronoun zich typically sits as close to the conjugated verb as possible, the adverb perfect gets pushed further back, right before the infinitive at the end of the clause.