She's unlikely to get a student visa at her age, unless it's for an advanced degree. You mention a Masters for you but she doesn't need an advanced degree to be a nurse. I don't think two foreigners can marry in China, so maybe in South Korea, once the divorce is final. For your situation, the spouse visa is a much better fit.
All that said, it takes as long as it takes, and NO, you don't qualify for DCF based on what you said. The members here quickly learn that separation is a fact of life in spouse immigration. It doesn't have to be always, but I don't see a way around it for the two of you, unless you find a way to wait it out with her outside the USA.
Start by clicking on the word "Guides" at the top of any page here.