LOL, I can't help but laugh. This brings back a lot of memories. I typically took things of the sort with grain of salt, but the questions I was asked most often were:
1) Do you like Kimchi?
2) Do you like Korean Woman?
3) Do you have girlfriend?
4) Can you teach me English?
5) Do you have a perm? (I had decided to grow my hair a bit longer, and it's wavy as opposed to being straight).
Nothing offensive that I can remember.