Great questions and the reporting period isn't overly explained for a reason. I want people to write in my world with confidence, to change the rules to fit their story.

Loosely they have seven days to report in. The punishment for being a runaway is a Bloodline Culling but it doesn't happen immediately. The family will be detained pending investigationd and attempts to find the Animal come before execution. The watches are very difficult to remove, they simply aren't designed to be taken off without special tools, so tracking an Animal almost always works.

During disasters, the report period is suspended based on the whether an Animal is registered as living in an affected zone. The System prioritizes rescue over slaughter.

As for false conversions, the Monday Lottery is always at 12:00 on the dot depending on timezone. It's the only legal time that conversions can happen.

Any conversion after that time is either punitive, the cause of a broken watch, or illegal.

Edward Hyde actually wrote in a malfunctioning watch and how the System handles it in big Culling Kennedy series.

I hope I answered your questions well enough