Now I am worry, she said December, and it was in December when I had my FP done and for some reason I am worry about that she mistakenly was talking about my FP got cleared? Am I just worried too much?
Yes you worry "too much", I think FP and name check are simultaneous processes and independent of each other, while you were waiting for FP, name check was being cleared, congrats, check your mail box twice daily nad call me if you are not better in 2-3 months. See my timeline, it verifies what I wrote.