"What's the weather like today?"
Translation:¿Qué tiempo hace hoy?
"¿Qué tiempo hace" is the set expression for "How is the weather?" or "What's the weather like?" The answers could vary: Hace buen tiempo (It's nice weather), Hace calor (It's hot), Hace mucho viento, (It's very windy), and the like. However, there are some exceptions like Está lluvioso (It's rainy).
That's always the case. I think the "correct answer" is taking a shot at giving the correct answer that's closest to your input, while the answer in forums is the default right answer. I think. Whether this is a good way to teach is another topic.
It couldn't work. "Qué hace el tiempo hoy" means "What is doing the weather".