1. Why's he late again?
2. Why is he late again?
[Are both okay? Is #1 commonly used?]
3. Why's he been working till late?
4. Why has he been working till late?
[Are both okay? Which one is commonly used?]
All the questions are fine.
In speaking, 2 and 4 are what you are most likely to hear, but in writing, 2 and 4 are used.
I think the only time I've seen "why's" is in a book's or short story's dialogue.