Just a reminder - cuál can mean "which" or "what". Many people might see this sentence and think to use "Qué", but this would sound weird to a native speaker, as if you were asking what the meaning of the phrase "your diagnosis" is. A while ago, I was texting my exchange student from Spain and I asked her "¿Qué son tus libros favoritos?" and she corrected me and said it should be "Cuales son..." because "Qué son..." sounds like I'm asking "What does 'your favorite books' mean?" So cual isn't just an alternative to qué; in this context, it's wrong.
From my understanding of it, "cuál" is "from a limited set of options," whereas "Qué" is more open ended. "Cual libro es su favorito?"= which (of all of the books created) is your favorite. "Que es su nuevo libro sobre?"="what is your new book about?" Gives you unlimited options and therefore justifies the use of "que"
Sí, se puede traducir como su o como tu. Si le estamos preguntando a un doctor que no conocemos, por un paciente (tal vez un familiar), lo normal sería: Doctor, ¿cuál es su diagnóstico? Si el doctor fuera mi hermano o un colega cercano, tal vez si le diría: ¿Cuál es tu diagnóstico? Espero te ayude el comentario. Saludos.
It's one of those words that can be translated into more than one English word depending on the situation.
Simple. "Su" applies to any gender. None need be found out.
The way Spanish works is that in a converstation exactly who is being talked about is mutually understood at the beginning of the conversation. It is established. And from that point on pronouns are used to refer to that person. The Duolingo sentences do not include the start of a conversation. This means that "su" in the Duolingo sentences applies to all possible meanings of "su" and it is all of them we need to learn. So there never is a particular gender unless the sentence solidly shows the gender at its own beginning. For example, " Ella quiere que su propia casa." She wants her own home.