Is COVID-19 present in urine and stools from infected victims? Does aerosolization from flushing in public restrooms pose a particular danger?

All of these things are true, and this is an insightful awareness based on your own creativity you have applied to this issue in the past, to realize the great potential of aerosol formation from flushing toilets to convey excreted organisms into the air, and also to greatly increase organisms present on surfaces within a public washroom, or private for that matter, so the fixtures may end up being coated by viable organisms. Much depends on the lability of the organisms in question to survive on a dry surface for a sufficient length of time to be picked up by an unwary human.