Everything about the exact timbre of your voice is captured in the waveform that represents it. To the extent that the sampling rate and bit depth are good enough to mimic your actual voice without introducing digital artefacts (something analogous to a pixelated image) that’s all it takes to reproduce any sound with arbitrary precision.

Timbre is the result of having a specific set of frequencies playing simultaneously, that is characteristic of the specific shape and material properties of the object vibrating (be it a guitar string, drum skin, or vocal chords).

As for how multiple frequencies can “exist” simultaneously at a single instant in time, you might want to read up on Fourier’s theorem and watch 3Blue1Brown’s brilliant series on differential equations that explores Fourier series https://www.youtube.com/watch?v=spUNpyF58BY

Yes digital media, and computers in general, are miracles of science and engineering. Is there some reason digital audio in particular inspires you in this way, as opposed to digital images?

Long list of numbers in sequence. Each represents how far away from equilibrium the speaker cone should be, at each point in time, as it vibrates back and forth.