There is a famous experiment , where a person gets 100$, and have to offer an arbitrary percentage of that to a stranger. If the stranger declines, both get nothing.
From the strangers perspective, getting offered even 1$ is a win, but the vast majority rejected anything below 30%
No. It's not a magic invisibility field inside. It's a magic object that works only on living "intelligent" creatures. It also doesn't work the same on different races. Only humans (hobbits are a subtype of human in Tolkiens lore) turn invisible. And because it's magic it also turns their clothing etc invisible. So either Frodo and his poop is invisible or nothing is.