@Bochulaz
No way she's 28. I checked back to the early chapters and when she first appears in chapter 2 he describes her as "a girl his age", which he had previously stated to be 15. If her zodiacal birth year is compatible with being 28, then she must have been born the next cycle and be 16.
The school thing isn't that big an issue. She's from a very wealthy family anyway, so private tutors are a likely explanation, and in any event high school isn't mandatory as far as I know.
Her alcohol is the problem, since I'm pretty sure Japan's drinking age is 20.