Learn Finnish: Tämä arvoesine on virheetön, ja sillä on aitoustodistus. - This valuable item is flawless, and it has a certificate of authenticity.

It comes from the noun virhe (mistake, flaw). When adding the -tön suffix (meaning "without" or "-less"), the final -e of the word becomes a double -ee-, making the stem virhee-. So, virhe + tön becomes virheetön (flawless).

Why do we use sillä instead of tällä when referring back to tämä arvoesine?

While the first clause uses tämä (this), the second clause refers back to it simply as "it", which is se in Finnish. To say "it has", we put se into the adessive case, giving us sillä on. Using tällä on would sound like you are pointing to it again ("this one has").

What are the parts of the compound word aitoustodistus?

It is made of two nouns: aitous (authenticity) and todistus (certificate, proof). Aitous itself is formed from the adjective aito (genuine, real) plus the noun-forming suffix -us, which is similar to the English suffix "-ity" or "-ness".

Does arvoesine just mean "valuable item" or is there a more literal translation?