The Duchess was sentenced to death for boxing the Queen of Hearts' ears.
`It's--it's a very fine day!' said a timid voice at her side. She was walking by the White Rabbit, who was peeping anxiously into her face.
`Very,' said Alice: `--where's the Duchess?'
`Hush! Hush!' said the Rabbit in a low, hurried tone. He looked anxiously over his shoulder as he spoke, and then raised himself upon tiptoe, put his mouth close to her ear, and whispered `She's under sentence of execution.'
`What for?' said Alice.
`Did you say "What a pity!"?' the Rabbit asked.
`No, I didn't,' said Alice: `I don't think it's at all a pity. I said "What for?"'
`She boxed the Queen's ears--' the Rabbit began. Alice gave a little scream of laughter.
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No. Alice is not royalty. At least, there is no mention in either of the books to suggest that she is, so it is reasonable to assume that she isn't. In Chapter 9 of Alice's Adventures in Wonderland, Alice decides that "When I'm a Duchess...I won't have any pepper in my kitchen at all." (But she doesn't say it in a very hopeful tone) From this it can be inferred that her current rank is certainly below that of Duchess and that she is probably a commoner.
The Cheshire Cat is usually thought of as the most agreeable character in Alice's Adventures in Wonderland. He is not unpleasant to Alice and, during the croquet match, she goes so far as to describe him as a friend.
In the book Alice's Adventures in Wonderland, the Duchess' baby turns into a pig, although it is never revealed how or why this happens.In Tim Burton's 2010 movie, the Red Queen uses a pig as a foot rest.
There are no 'bad characters' as such in Alice's Adventures in Wonderland - no villains, no bad guys - but the Duchess and the Queen of Hearts are the most unpleasant characters who Alice encounters.
Alice in Wonderland the Seccond was made in 1951