Which is the shortest duration for a pitch difference in audio signals to be perceived by the human auditory system?
It really depends on what you mean by difference in pitch. Subjects can discriminate differences in frequency for very short tones, but it does not mean they are being perceived as pitch differences. The classic paper in this area is Moore (1973):



As the duration is reduced from 200 ms to 6.25 ms, performance falls off, especially for low frequency tones. It is worth noting that creating extermely short sounds with narrow bandwidths is difficult. With a 12.5 ms duration, subjects can still discriminate between tones with frequencies of 250 Hz and 255.7 Hz (a Delta f of 5.7 Hz and a (Delta f)/f of 0.023).

C4 has a frequency of 261.63 Hz and C4# has a frequency of 277.18 Hz for a Delta f of 15.55 Hz and a (Delta f)/f of about 0.06. One would expect that you could discriminate C4 from C4# with durations substantially shorter than 12.5 ms

In regards to your "bonus question", when the stimulus consists of two tones, things get very complicated. Judgements like can you hear both tones are very different from can you hear the difference between a single tone and the pair of tones.