No one said that it did. Your basic issue is that you cannot separate facts from inference.
It is, but you don't see why. You see, the orbit tells you from where the comet originated. And all the short-term comets originated in the Kuiper belt.
Actually, it does. A collision with a planet or an asteroid would destroy all but the largest Kuiper objects. And it's easy to determine whether or not a planet was close enough to significantly alter it's motion.
I'm pleased that you now understand this.
How many orbits do you think we can't accurately determine?
Turns out we do know this. And the composition of such objects varies in much the way that comet compositions vary:
http://web.gps.caltech.edu/~mbrown/out/kbcomp.pdf
https://www.lpi.usra.edu/education/explore/comets/background/
Why would you think that? Until a comet comes close to the Sun, any oxygen within the Kuiper object would be trapped because of frozen gases covering the object.
No. The Kuiper Belt was predicted based on the paths of short-term comets. Pluto was thought to be a lone planet, the only object in the outer solar system. Kuiper predicted a belt of icy objects out beyond Pluto. Which turned out to be true.
It merely explains the reason we continue to see short-period comets.
It merely explains the reason we continue to see short-period comets.