Questions & Answers about Yo no trabajo hoy. ¿Y tú? Yo tampoco.
Why does it say trabajo (I work) instead of something like "I am working"?
In Spanish, the simple present tense (trabajo) is often used for things happening right now or around this time, like today. While English prefers "I am not working," Spanish naturally says no trabajo to mean the exact same thing.
Since Spanish verbs already tell you who is doing the action, why use yo here instead of just saying No trabajo hoy?
You can definitely just say No trabajo hoy! Including yo adds emphasis. Because the speakers are comparing their schedules, using yo makes the contrast clearer: "I am not working. Are you?".
How exactly does Yo tampoco mean "Me neither"?
Why is it ¿Y tú? instead of something like ¿Y ti?
When asking "And you?", you use the subject pronoun tú because the full hidden question is "And do you work today?". Since "you" is the one doing the action, you need the subject pronoun.