Regarding Sylphy having sex with Kosuke in the second chapter it is explained later, chapter 5 I think. According to the common sense of that world, "political marriages" are normal and based on that common sense, it's normal that she gives him her first time as form of marriage. She does it because she wants to ensure that he, and his manufacturing ability, stay with her. And here comes the catch, since she was a princess of a kingdom destroyed by that "Holy Kingdom" that was spoken of in the first chapter, and she wants or has to get it back and rebuild it. That is one of the reasons why she sleeps with him, the other reasons I think are obvious, in the short time she has known him she has realized that he sees her simply as Sylphy, while the rest of the people see her or as "the problematic little princess" or "THE PRINCESS of our kingdom".