Learn Polish: Dlaczego to ciasto smakuje sztucznie? - Why does this cake taste artificial?

This is a major difference between Polish and English. English uses adjectives with sensory verbs like taste, smell, and look (e.g., 'tastes artificial'). Polish treats these verbs as actions, so they must be modified by adverbs. You are literally saying the cake 'tastes artificially'.

Can I ever use an adjective to describe how food tastes in Polish?

You can, but you have to change the phrasing. Instead of the verb smakować, you could use mieć (to have) and the noun smak (taste). For example, Dlaczego to ciasto ma sztuczny smak? (Why does this cake have an artificial taste?). Here, sztuczny is an adjective modifying the noun smak.

How do I say it tastes like something else, such as 'it tastes like plastic'?

To compare the taste to a noun, use smakować jak followed by the Nominative case. For example, to say it tastes like plastic, you would say: To ciasto smakuje jak plastik.

I remember learning that smakować takes the Dative case. Why isn't there a Dative word here?

You use the Dative case when you want to specify who likes or experiences the taste, like in To ciasto mi smakuje (This cake tastes good to me / I like this cake). Our sentence is asking an objective question about the cake's flavor in general, so no person (and therefore no Dative pronoun) is needed.