Question: Anastasia basically lost most of her memories from hitting her head, as well as the possible trauma of what happened to her the night her family was killed. Could someone really lose most of their memories that way?
Answer: Amnesia exists, but it is a temporary condition. It does not last for the long-term and people usually regain their memory in a day or two, sometimes up to a week. Extreme cases can last longer, but not in the way it is depicted in movies. Some people may lose memories due to severe brain damage from a traumatic injury, but that is permanent.
Question: Why did Pain and Panic run and leave baby Hercules on the ground when they hear Alceme and Amphitrion instead of grabbing the baby and running?
Answer: When the couple turns the corner, startling Pain and Panic, they proceed to...well...panic. Pain and Panic didn't want to be found out. And while carrying a baby, they couldn't hide as quickly or as nimbly. It was an impulsive act which they might not have committed if they had time to think it out rationally. Besides, had they not panicked and run, baby Hercules would have ended up in the hands of Hades and the movie would have been over before it began.
Answer: It's unknown how long Belle was at the castle. This sequel, The Enchanted Christmas, was made as an afterthought to the original Beauty and the Beast film, and there was no consideration or explanation about how this would fit into the original timeline. This is a stand-alone film, and it is typical of how the more popular Disney animated films, such as The Little Mermaid, Aladdin, etc. have added-on stories that are usually released straight-to-video.
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