Thank you for such a long and thoughtful post! I haven't seen the Canfield, so I can't comment on that, but I can give you one woman's answer to your questions:
1. Where do the rats in Maria/Clara's dream come from? She just goes to bed on Christmas night and dreams of rats?
Yes. Rats and mice were a part of every 19th century household. So this doesn't necesarily have a deep psychological significance. If you were a 10 year old girl and a mouse ran over your foot on a regular basis, you might dream of them too! (There are stories about the theaters of that day that people in the stalls -- orchestra to us -- took umbrellas to performances to beat off the rats.)
2. What makes this Nutcracker Doll so great that it becomes her prince in her dream?
He's an enchanted prince, and she knows this because she's breen brought up on fairytales.
3. Who is this Snow Queen and cavalier? Where do they fall into the picture?
who is Dewdrop? Why is she dancing what is her purpose?
They don't have a dramatic purpose. They're divertissements. This ballet comes from the ballet feerie tradition, and the divertissements are thematically related to the story, but not dramatically so.
4. Why, besides the fact that kids like candy, is Clara taken to the land of Candy?
Same reason -- a divertissement. Although if you'd like to read more background on this, Mel Johnson has done an excellent historical summary of Nutcracker that's on our main site
here5.Who is this Sugar plum Fairy person? Who made her the ruler of Candyland?
Not to be taken literally. It's thematic, not dramatic. If you're doing a ballet with a divertissement set in a Kingdom of the Sweets, you need a ballerina.
I think Petipa/Ivanov were operating under different assumptions and from within a different tradition. These are all good questions if you're coming to Nutcracker wanting a narrative ballet that makes contemporary dramatic sense. But it was made as a ballet that appealed to the senses, that didnt tell a story in a literal way, but left a lot of scope for imagination. Someone might read all kinds of things -- relationships among the characters, what does Tea really symbolize, etc. And others might view it as a poem. Why does Robert Frost write of Snow, and stopping by the woods? Is it really about winter? Or about his inner life, his time of life, using the beauty of nature and imagery to make his point. If one thinks of Nutcracker and Sleeping Beauty as poems, one asks different questions.