Which Alice?

ALICE IN PUZZLE-LAND
"So Humpty Dumpty didn't solve it," said Alice.
"Oh, yes, he did, because he asked me another question, and
when I answered, he was able to solve it."
"What question was that?" asked Alice eagerly.
"Unfortunately I have forgotten by now," replied the White
Knight.
"It is very difficult to get information from you," said Alice.
"Don't you remember anything about the question?"
"Yes," replied the Knight, "I remember that Humpty Dumpty
either asked me whether any two consecutive statements were true,
or he asked me whether any two consecutive statements were false,
but I can't remember which of the two questions he asked, or what
answer I gave."
Which of the three defendants was guilty?
THE NEXT TRIAL "I remember another curious trial," said
the White Knight. "It involved three defendants. Each of the three
accused one of the other two. The first defendant was the only one
who told the truth. Had each one accused someone different, but
again not himself, then the second defendant would have been the
only one who told the truth."
Which of the three defendants was guilty?
THE NEXT TRIAL "Another trial I know about," said the
White Knight, "is one in which I was not present. It was told to me
by the Jabberwocky.
"As the Jabberwocky explained, there were again three defendants.
Each of them accused one of the others, but the Jabberwocky
didn't tell me who accused whom. However, he did tell me that the
first defendant told the truth."
"What about the second defendant?" asked Alice.
"The Jabberwocky never told me whether the second defendant
told the truth or lied."
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