Regarding how the narrator knew his sister died, there’s also this:
The sister was on life support of some kind. The “knowledge tinted in red” that he had difficulty processing was his sister’s vitals shown to him through a monitor, the information presented in red hues. From this information, he knew when his sister died. This also gives him a motive - taking care of his severely ill sister was frustrating him, and he sought to get rid of the responsibility that was dragging him down, but could not bear to do it himself, so he had a serial killer do it. Maybe the little object he knocked off the table that was important to his sister was a bottle of medication.
Though that’s a bit far-fetched compared to your suggestion.