Yes, it is possible for audio files with variable tempo or with silent pauses. In this case BPM Counter could not detect BPM and return zero value.
A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. In some cases second harmonic may have higher magnitude, so BPM Counter will return double BPM value.
BPM Counter support only WAV and MP3 audio files, it will not see MP4 files from iTunes.
BPM Counter can save BPM values inside ID3 tags, so any software could access them.