Learn Finnish: Hänen äänensä värähti, kun hän vastasi kysymykseen. - Her voice quivered when she answered the question.

Värähti is the past tense of värähtää. The suffix -ähtää adds a sudden, brief, or one-time meaning to an action. While the related continuous verb väristä means to tremble or vibrate ongoingly, värähtää means to quiver just once or very briefly, which perfectly describes a sudden catch in someone's voice.

Why is the word for question, kysymys, in the illative case here?

This is a verb rection rule that learners often need to refresh. The verb vastata (to answer) always requires its target to be in the illative case (into). In Finnish, you literally answer into a question, hence kysymykseen instead of the partitive or allative case.

How does the stem of kysymys change to become kysymykseen?

Nouns ending in -us or -ys that are derived from verbs (like kysymys from the verb kysyä) change their final -s to -kse- before adding most case endings. To form the illative case, you take this kysymykse- stem and add the -en ending.

Is the possessive suffix -nsä strictly necessary on äänensä if the sentence already specifies Hänen?