Far be it for to tell you what is or is not, but perhaps I can shed a little insight.
Her behavior is not that strange. She is young, Japanese and dealing with a wide range of customs, values and feelings that may go against what she has been taught.
Relax. You like her and I advise that the best medicine is that of friendship. When you have a chance you can try letting her know that you like her and would welcome getting to know her better, and at the same time be willing to be friends.
Think of a pressure cooker: Remove the pressure and the cover comes off easily, rush it and it will blow up in your face.
As for her family, their behavior is also normal. First it may very well be that your “blackness” caught them off guard. That does not mean that they do not or cannot learn to like you. Second, your skin color may mean nothing to them, but the fact that you are a “guy” interested in their daughter may call for sever scrutiny. Don’t sweat it. It is her parents, so let them act their part.
The young woman seems interested. The touching and coming close and such, for some young Japanese women, is a major deal. She is showing you public affection. That is a biggie. Her ditching you when other Japanese or friends come around may be because it is shameful to show public affection. This is a common notion to many Japanese. It is true that it has changed for some, yet for many it is still a tough one.
I have a Japanese girlfriend, grown woman (I will not reveal her age.), and after two years she is still a little distant when her friends are around and when her family is anywhere in sight, you can forget us being close. And they know me and like me!
Take it easy. Enjoy the friendship even if it does not pan out into more. By being supportive in friendship, you establish by your actions that you can be supportive in a deeper relationship. You know she is watching you, so let her see your true self.