None of those involve something as odd as buzzing your lips. Unlike other instruments, kids generally don’t even figure out how to play brass unless they are taught. Most think you’re just supposed to blow, and can’t figure out what they are doing wrong.
I think the other interesting question is what got us from instruments like the serpent and the trombone (no valves, just ways to manipulate the length) to the common three or four valve instruments we know today.
I think you underestimate people’s ingenuity. My son was buzzing his lips for fun at age one. It just takes someone to happen to do it while putting a tube up to his lips to see the effect.
Don’t know, but I’d guess it followed development of the valves needed for pipe organs.
Your momma has, to name but one. 
One step towards this was the French horn. It can already play a more nearly diatonic scale than the trumpet can, for assorted reasons that allow it to play the higher harmonics at the expense of brilliance. Since its bore is nearly cylindrical for much of its length, it was no great stretch to allow it to have a removable section that could be swapped out for one of different length - turning your horn in F into a horn in D, C or whatever, since a different-length pipe will play a different harmonic series. The player needed notice, though - an instruction in the score like “Mutano in G” meaning “Change to the G-crook”, and thirty bars rest. Once you had this, it was a small logical step, albeit a long technological one, to devise valve-gear that would let you do this on the fly, and have your spare crooks built in even when not in service.
Brass instruments could be made with finger-holes like the woodwind had, but this turns out to cost more in tone than the increased flexibility really makes up for. So the key-bugle was never more than an interim measure… and for that matter the natural trumpet has its adherents to this day.
As to “middle ages”, the sackbut - forerunner of the slide trombone - didn’t come along until the Renaissance; valve brass came later.
Shofar shogood.
Now, now. There’s no reason to bring the Kardashians into this.
My grandson has been buzzing his lips for a couple of weeks and he’s barely five months old. He’s clearly gifted! 