Why? You know that it's possible to write every waveform, as short as you like, as an infinite sum of sinusoidal plane waves.

You should be more accurate if you want to get it right.

Fourier ANALYSIS takes a repeating waveform and replaces it as an infinite series of harmonically related sinusoids.

The Fourier TRANSFORM can be carried out on any function. The FT of a sinewave (in the time domain)which has been modulated by a pulse (i.e. a burst of sinewave) has a peak (in the frequency domain) at the 'carrier frequency' and, potentially, a continuum of sidebands (sinusoids of infinite duration) which stretch out on either side. The shorter the pulse in time , the more the spread of the sidebands in frequency.

you have the interference pattern even sending individual photons; how would you interpret this fact?

The two slit interference pattern would give a density pattern, corresponding to the probability of a particle / photon hitting a particular bit of the screen. That is the same pattern as the wave interference approach would give. (As the probability density function of the electron around the atom relates to the wave function.)*

The detailed pattern, seen on the screen (i.e. the actual spacing of the half power points, for instance) would depend on the range of frequencies (bandwidth) of the light / population of photons. It would be interesting if someone had compared the detailed interference patterns from different sources. Ah, yes, of course there would be spectral spreading due to Pauli exclusion - as with high pressure sodium lamps.

No two photons would be of the same frequency - even in a low pressure gas .- Also, because of Heisenberg uncertainty, you could not be sure of the precise frequency of any photon.

As for the lifetime of a photon McQueen, - it can be as long as you like - but, once you have measured it, it is ended. It starts life 'sometime', when an atom (or system of atoms) changes energy level and it ends when it has interacted with another system. (Yes, Lightarrow -I have just read your post)

*You get the same thing with electrons interfering as they pass through a thin carbon sheet.