vomit is usually liquid or heavily digested stuff. feces is compacted and excreted. my imagination maybe a little specific here but so is the description "fully formed feces"
If your intestines are obstructed, and the fecal matter has started forming, and it's trying to come out, where do you think it will come out from?
When there's no place for the compacted feces that's building up to go (due to a failure in peristalsis, for instance), it backs up into the the stomach, which naturally irritates the stomach and causes the person to vomit the contents, which includes their feces.
I wouldn't wish it on anyone.
It doesn't sound particularly possible.
This is entirely possible. See copremesis, ICD10 code R11.13.
It usually occurs due to intestinal blockage or fistulae.