It would've been great if it had gotten a few more chapters, not a full serialization, but just a few more chapters. To flesh out the story some more and so on.
About the king asking her about political affairs - I just assumed that the prince has told the king beforehand about MC being very gifted and stuff. And the king asked the questions just to see how gifted and smart she is.
At least that's how I reason that scene to myself lol