) Don't check the box that doesn't allow people to reply to your post if you do want answers, okay?
2) "He's a day off" isn't idiomatic. Although "he's" used as a contraction for "he has" it's only used with another verb. He's been so happy since he met you but not He's a day off.
3) Your original question: Are you off today? Do you have today off? Are you working today? Do you have to go to work today?