The theme that always struck me from this episode is "The Hero With the Thousand Faces" by Joseph Campbell. Briefly put, the major focus of this is the search for the father. The hero has to go through a series of adventures and challenges before he can meet and discover the meaning of the father.
In this episode, of course, it is Annabelle who is searching for her father. She undergoes a series of adventures and trials and, at the end, she maybe realizes that she already has within her the knowledge the father might have imparted.
Of course, in Campbell's classic, the hero goes through some pretty tough stuff. It may be interesting to some to know that George Lucas was a protege of Joseph Campbell, and based his story of Luke Skywalker on "Hero With a Thousand Faces." Luke's trials and tribulations were a lot more dramatic and life-threatening than Annabelle's, of course, but the same myth underlies both stories.
Ghislaine, I think the other "quests" you mention are secondary to the main story, the monomyth of the search for the father.
I'll also mention that this is not one of my favorite episodes. Maybe part of that is because Heyes is secondary here, and I am a Heyes girl forever. But Annabelle, in my opinion, was a bit of a whiner and a baby. It wasn't till the end, when she admits that she's not quite grown up to deal with the reality of her father, that I start to like her, and maybe even identify a bit with her.
Anyway, that's my humble opinion.
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"If it's worth doing, it's worth doing badly."
"The failure in doing something is stopping too soon."