Learn Polish: Uprzejmość nic nie kosztuje.

It is built from the adjective uprzejmy (polite). By removing the adjective ending -y and adding the suffix -ość, you create the abstract noun uprzejmość (politeness). All Polish nouns created with the -ość suffix are feminine.

Does the abstract noun uprzejmość have a plural form?

Like many abstract nouns ending in -ość (such as młodość or miłość), uprzejmość is generally uncountable and rarely used in the plural. If you want to talk about multiple instances of politeness, you would usually rephrase it to something like uprzejme gesty (polite gestures).

Negated verbs usually require the genitive case. Why do we use nic instead of the genitive niczego here?

While a negated direct object normally takes the genitive, the pronoun nic often stays in the accusative form in everyday speech, especially in fixed sayings like nic nie kosztuje. Using the genitive niczego nie kosztuje is also grammatically correct, but sounds unnecessarily formal here.

Does nic nie kosztuje literally mean 'it doesn't cost nothing'?

Yes! Polish strictly uses double negation. Whenever you use a negative pronoun like nic (nothing), nigdy (never), or nikt (nobody), you must also negate the main verb with nie.