Is this hearsay evidence admissible?There is a bomb threat at school. Anne testifies that she was standing in the school hallway when she heard a...

The answer to this depends on the way in which these
statements are going to be used.

As the link below tells
us, hearsay can be admissible if all that the attorney is trying to prove is that some
statement was made (not that the statement was true).  The link says that hearsay is
permissible if the attorney wants the judge or jury

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...to consider the fact that a certain statement
was made, but not the truthfulness of that
statement...

So, Anne's
statement would not be admissible as proof that a bomb was planted.  It would be
permissible as proof that someone said a bomb had been
planted.  It can prove the existence of the statement but not its
veracity.

Jacob's second statement is likewise permissible
as long as it is being used to shed light on Anne's credibility.  The fact that she took
those actions would imply that she did not actually know who had planted the bomb.  This
could be used to impeach her testimony.