Learn Spanish (Latin America): El apocalipsis es inminente, pero el superhéroe tiene sueño. - The apocalypse is imminent, but the superhero is sleepy.

You are right that most Greek-derived words ending in -sis are feminine (like la crisis, la tesis, or la síntesis). However, el apocalipsis is a rare exception that is masculine. Another masculine exception you might encounter is el éxtasis (ecstasy).

I know we use tener sueño for "to be sleepy," but is there an adjective I could use with estar instead, like in English?

Yes, but it is much less common in casual conversation. You could say el superhéroe está soñoliento (the superhero is drowsy). However, Spanish speakers overwhelmingly prefer the "to have" structure for this physical state, so tiene sueño (literally "has sleep") is the most natural choice.

Why does superhéroe have a written accent mark on the e?

It has to do with how Spanish breaks words into syllables. The vowels o and e are both "strong" vowels, so they don't blend together into one sound. Instead, they stay separate (su-per-hé-ro-e). Because the spoken stress falls on the third-to-last syllable (hé), it requires a written accent mark according to Spanish spelling rules.

Since this lesson covers reassurance with ya + future tense, how would we tell someone not to worry because the sleepy superhero will eventually save us?