When is Kato’s next day off?
During lunch break, I ate shaved ice at a cafe.
Tomorrow is my day off, so I’m planning to play Mario Kart by myself for the entire day.
The kanji rest has a little hiragana attached, but it's nothing that would suggest it's anything but a noun (it is!). It means the same thing as the kanji, rest.
Since this word is made up of a single kanji with some hiragana, it should use the kun'yomi reading. When learning the kanji, you didn't learn that reading, so here's a mnemonic to help you with this word:
So, do you want a rest from work or school? You should say "Yes!" (やす).