In Act 3, show how the following add to the conception of Hamlet's charactera.) the "to be or not to be" soliloquy b.) His advice to the...

Well you do have a logical break down of the events of Act 3
here and this is the privotal act of the play, so we learn a lot about Hamlet in Act three.  Here
is one comment on each section -- but there is definetly more that can be said about Hamlet's
character as it is revealed in each of these events.

1.  The "To be
or not to be" soliloquy reveals Hamlet's philosophical nature as he contemplates life and death
and action and inaction.  His concluding statement does explain how actions sometimes don't
happen because thinking about the consequences takes over the emotional
drive.

2.  His advice to the players reveals his experience with
theatre and with the act of "acting."  He cautions them to act naturally -- don't over
act.

3.  His speech to Horatio reveals his trust in his friend. 
Together they are going to be on watch for Claudius to reveal his guilt in the murder of King
Hamlet.  Prior to this scene, Hamlet had kept all that to
himself.

4.  In his conversation with Rosencrantz and Guildenstern
he reveals his contempt and complete distrust of them.  By using the recorder (a simple intrument
to play) and suggesting that if they can't make music with that they CERTIANLY will not make him
"play" or "reveal himself" he is showing a clever mind and his
anger.

5.  When Hamlet thinks he sees Claudius in prayer he decides
not to take his revenge at that time.  He reveals his logical and moral mind when he explains
that killing Claudius when he could go to heaven would not be a very good revenge of his father's
murder.

6.  Hamlet's killing Polonius reveals that Hamlet is, in
fact, capable of rash behavior and of actually killing someone.  Granted he thought it was the
King, but he still did it!  His rather cold justification of the murder also reveals his attitude
about Polonius.

7.  His long speeches to his mother reveal his utter
disgust with her marriage to Claudius.  He just can't understand how she could go from being
married to a great man like his father to a gross man like Claudius.  He is logical, though a bit
condescending I think, in his advice to his mother to "quit the habit" of being with
Claudius.