Learn Finnish: Kumpi pysti kimaltaa enemmän, kultainen vai hopeinen? - Which statuette sparkles more, the golden or the silver one?

They act as an appositive phrase or trailing clarification for the head noun pysti. Because pysti is in the nominative case (acting as the subject of the sentence), this trailing phrase must match its case. If the head noun were in a different case, the apposition would change to match it, for example in the partitive: Kumpaa pystiä katsot, kultaista vai hopeista?

Could I use mikä instead of kumpi in this sentence?

No. Because there are exactly two options presented (kultainen or hopeinen), you must use kumpi ("which of the two"). The pronoun mikä is used when choosing from three or more options.

Why does this sentence use vai instead of tai for "or"?

Vai is exclusively used in direct questions where the options are mutually exclusive and the listener is expected to choose one over the other. Tai is used in regular statements or when presenting inclusive choices.

How do the adjectives kultainen and hopeinen relate to the nouns for gold and silver?

By adding the -inen suffix to the base nouns kulta (gold) and hopea (silver), you create adjectives that describe a noun as being "made of" or "colored like" that material.