Learn Finnish: Monet näyttelijät ovat liikuttaneet marionetteja naruilla. - Many actors have moved marionettes with strings.

The verb liikuttaa is a transitive causative verb meaning 'to move something else'. Liikkua is intransitive and means 'to move oneself'. Since the actors are moving an object (the marionettes), the transitive liikuttaa is required.

Why is marionetteja in the partitive plural rather than the accusative?

The partitive is used for the object here because the action of moving the marionettes is irresultative (it has no specific endpoint or completion described) and it refers to an indefinite number of them.

We are learning about exclusive group size adverbs ending in '-staan/-stään'. How would I say the actors did this 'by themselves' (alone)?

You could add the adverb yksistään (alone / by themselves) to the sentence. If you knew the exact number of actors acting as an exclusive group, you could use a word like kolmestaan (the three of them together).

Why does 'with strings' translate to naruilla using the adessive case, rather than using a postposition like kanssa?

In Finnish, the adessive case (-lla/-llä) is used to indicate the tool or instrument used to perform an action. Using kanssa would imply company, as if the actors and the strings were moving the marionettes together as partners.