OK. This pushed most of my buttons. When I hear UX designers talk about design thinking, they're talking about working with their own team to "break" a problem and generate ideas. But design thinking came about before UX was UX. And it is collaborative (yes) co-creative (yes), but it is also community-driven, much more so than it was in the early IDEO days. I use design thinking to work with non-designers to help them (ordinary folk who live and work in communities) to see community challenges differently and, perhaps, have some really groundbreaking thinking around them.
So, no, Design Thinking is not always an "ideation first" process. Quite the opposite. And this relates to number 2. Design Thinking does anything BUT accept problems at face value. I use Design Thinking tools to help people reframe problems and to see them in entirely different ways.
When you say "questions and problems have two 'sides'", I can tell you that, when I describe a question to people I ask them to think of it as a multi-faceted gem. As you turn it in your hands it absorbs and reflects light on each of those facets. You experience the shape in your hand and what if feels like when you turn it. Every movement is a different way for you to view the "question".
And I'm baffled that you say that Design Thinking is solution-focussed. I say it is focussed on defining, redefining and refining a problem and then playing with tools that help you think about the problem in novel ways.
I agree that creating a problem is a generative and creative act. But I wouldn't stop there. It can also give you new perspectives on which to either begin again or to begin to ideate (at a later time) on possible solutions.