When I try to copy a tune or watch other people play the piano, I sometimes hear a note that isn't there. Especially top note is the case. My teacher said that it is related to harmonics, told me that if you smash down a c note, there are lots of sounds you can hear otherwise of just a c note. Then, my question is,

1) Is this occasional phenomenon normal and do you sometimes have the same problem as I do?
2) If you have absolute pitch, does this bother you?