Questions & Answers about Şu kadın bir mühendis.
How would I ask "Who is that woman?" based on this sentence?
To ask "who", you use the question word kim. In Turkish, the question word usually sits exactly where the answer would be. Since the answer in this sentence is bir mühendis, you replace it with kim to form the question: Şu kadın kim? (Who is that woman?).
Can I use ne to ask what her job is?
Yes! If you don't know her profession, you can ask Şu kadın ne? (What is that woman?). While asking Mesleği ne? (What is her profession?) is often more polite, using ne (what) directly in place of the job is grammatically correct and very common in casual speech.
Why use şu instead of o for "that woman"?
Both şu and o translate to "that". However, şu is specifically used when you are physically pointing someone out or directing the listener's attention to them right in front of you. If she were further away, or if you were talking about her in the abstract, you would use o.
Do I have to include bir (a/an) when stating someone's profession?
No, you don't! In fact, it is much more common in Turkish to leave bir out when talking about jobs. Saying Şu kadın mühendis is totally natural. Including bir is not wrong, but it can sound a bit like saying "That woman is one of the engineers."