Learn Finnish: Kuka luistelee taitavimmin tässä kilpailussa? - Who skates the most skillfully in this competition?

The base adjective is taitava (skillful). To form the superlative adverb ("most skillfully"), we take the inflectional stem taitava-, drop the final vowel a before the suffix, and add the superlative adverb marker -immin. This gives us taitavimmin.

Could I use the superlative adjective taitavin in this sentence instead?

No, because the word here describes the verb luistelee (skates), which means you need an adverb to express how they skate. Taitavin is an adjective and describes a noun. To use it, you would have to change the sentence structure to something like Kuka on taitavin luistelija? (Who is the most skillful skater?).

Why is the verb luistella conjugated as luistelee (singular) if there are many skaters in the competition?

The question word kuka (who) always takes a third-person singular verb in Finnish, exactly as it does in English. Even if you expect the winning answer to be a group of people, you still ask Kuka luistelee (Who skates).

Why do both tässä and kilpailussa have the inessive ending (-ssa/ssä)?

In Finnish, demonstrative pronouns like tämä (this) must agree in case with the noun they point to. Because "in the competition" requires the inessive case (kilpailussa), the pronoun changes to match it, becoming tässä.