Which is the shortest duration for a pitch difference in audio signals to be perceived by the human auditory system? If I have two short audio signals, for example pure tone C4 and C#4, so half-tone difference, how short can they be that the human can hear the difference in pitch? Was there any blind-experiment/research with a good set of subjects done about this?

I was causally testing with a short script and it seems I am able to distinguish down to 30 ms long samples if I play one sample, then one second of pause, and another half tone higher sample.

I can also do it for shorter, but I am not sure anymore if I really hear it, or if I just imagine hearing the difference.

Bonus question: how short can it be if the signal consists of two tones. So of both C4 and C#4 at the same time. Can one hear that there are both C4 and C#4 in the signal if it is only 30 ms long?
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.