Yeah! The "timbre" (which despite how it looks is said "tamber") of an instrument is its audio "profile". It's what makes a piano different than a flute, or on a more subtle level makes one piano slightly different from another.

But here's the nuts part: what makes up the timbre of an instrument is a bunch of different resonating bits all resonating together. Essentially the reason a flute sounds like a flute is because it comes "pre-loaded" with a boatload of simple waveforms already added together. When you play a note on one, you get the main pitch you're playing, but the instrument's body and your breath all also produce a whack-ton of side tones all playing at the same time. And like a fingerprint, our ear/brain hears all these bits start and stop together and says "that's a flute".

So it's the same process, really: simple bits adding together. But "flute sound" isn't the atom. It's made up of a bunch of simple waves already added together, which then gets added to the other sounds that sound like pianos or guitars, which produces the final mix.

I don't know if you'll get anything out of it, but you could look up videos of a "modular synth" setting up a trumpet sound or something. These devices have simple electronic tone generators, but by layering them and plugging them into each other, and using effects and the like, they can start to mimic the timbre of a trumpet or whatever. By essentially adding together the "key bits" of the harmonics (these other waves) they can start to approach the feeling of a trumpet sound, but just with simple, raw, parts.

In theory an infinite amount of different waveforms. But practically speaking, no one would be able to distinguish them by ear, and even oscilloscopes have limited resolution.

Music is super complex and can't even be described by a single or a few waveforms, unless it's very simple. Another simplified way to explain all the sounds of music fitting on one "waveform" is to imagine the high frequency stuff happening in between the low frequency stuff. And usually the different instruments and voices don't happen all at once, they happen slightly one after another, or in sync but intentionally so they affect each other the "right" way. Whatever the "right" way is...

Definitely, but you only ever perceive all that because of the one-dimenaional way your eardrums vibrate, and they vibrate because the air next to them vibrates. If we make the air next to your eardrums vibrate in the same pattern they did when the band were performing, you will hear and perceive the same sound as the band made.

You should be aware that an amplified band is only ever making sound at you through a bunch of speakers whose only function is to vibrate air in a one dimensional pattern.

Separating that all out into different instruments and people and timbres etc is the clever bit, and your brain does that, not the speaker, and you largely learned it as a child.