Learn Finnish: Kukaan ei tappanut merirosvoa.

Kuka means "who", but when you add the -an or -än suffix in a negative sentence, it becomes kukaan, meaning "nobody" or "no one". Remember that Finnish requires the negative verb (ei) to go along with it.

Since kukaan means "nobody", why is the negative verb ei in the third-person singular form?

In Finnish, indefinite pronouns like kukaan (nobody) and joku (somebody) are grammatically singular. They are treated just like hän (he/she), so they take the third-person singular negative verb ei.

Why is the verb tappanut instead of the regular past tense tappoi?

This is a negative past tense sentence. To say that someone didn't do something, you use the negative verb (here, ei) followed by the past participle of the main verb (the NUT-participle). For tappaa, that form is tappanut. You never use the regular past tense marker in negative sentences.

Why is the object merirosvoa in the partitive case rather than the genitive-accusative (merirosvon)?

This is one of the strictest rules in Finnish: if the sentence is negative, the object must be in the partitive case. Because the action didn't happen, merirosvo takes the partitive ending -a.