Learn Finnish: Läpinäkyvä esinekö lasinpuhaltajan täytyy jäähdyttää? - Is it the transparent object that the glassblower must cool down?

This is contrastive focus fronting. By moving läpinäkyvä esine to the front and adding -kö, the speaker is asking specifically if the transparent object is the thing that needs cooling, rather than something else. If it were a standard yes/no question, the clitic would go on the verb: Täytyykö lasinpuhaltajan jäähdyttää läpinäkyvä esine?

Could the clitic -kö be attached to the adjective 'läpinäkyvä' instead?

Yes, but it changes the exact focus. Läpinäkyväkö esine... asks 'Is it a transparent object...?' putting the focus entirely on its transparency. By attaching -kö to esine, the focus is on the whole noun phrase läpinäkyvä esine (the transparent object as a single concept).

Since 'läpinäkyvä esine' is the object being cooled down, why isn't it in the partitive or genitive-like accusative case?

It is a total object, meaning the whole object is being cooled. Usually, singular total objects take the genitive-like ending -n. But because this sentence uses the necessity verb täytyy, the total object must be in the nominative case. Seeing it at the front of the sentence makes it look like a subject, which is a very common trap!

Why is 'lasinpuhaltaja' (glassblower) in the genitive case here?