Learn Russian: Почему высокая активность прерывает цикл? - Why does high activity interrupt the cycle?

It comes from the root рвать (to tear). The prefix пре- adds the meaning of 'across' or 'inter-', making it 'to interrupt.' The perfective form is прервать.

Why is the imperfective aspect (прерывает) used here instead of the perfective?

The imperfective is used to state a general fact, rule, or recurring process. If the sentence was asking about one specific, isolated event in the future, it would use the perfective прервёт.

Is цикл in the nominative or accusative case here?

It is in the accusative case because it is the direct object of the verb. Since цикл is a masculine inanimate noun, its accusative form looks exactly the same as its dictionary (nominative) form.

How do we know the gender of активность just by looking at it?

While nouns ending in a soft sign (-ь) can be masculine or feminine, активность uses the suffix -ость. This suffix is extremely common for turning adjectives into abstract nouns, and words ending in -ость are always feminine.