In Act III of Macbeth, what is happening to each character mentally?
In the beginning of Act III, Banquo voices suspicion about Macbeth and Duncan's murder--their friendship is eroding.
Macbeth is planning the murder of his best friend, Banquo and his son, Fleance. Macbeth does this for two reasons: 1, Banquo and Fleance stand in his way for a long reign on the throne of Scotland, and 2, Macbeth knows Banquo suspects him.
Macbeth's hired murderers "safely dispatch" Banquo, but Fleance escapes. Macbeth is happy about Banquo, but he is mentally plagued by the fact that Fleance has escaped since the possibility of Fleance and/or his children usurping the throne from Macbeth exists still.
We also learn that Macbeth will be intentionally mislead by Hecate and the witches, and since Macbeth has mentioned to Lady Macbeth that he will consult the witches, the audience knows that this will cause him additional mental anguish.
Others in Scotland are beginning to suspect Macbeth's connection with Duncan's death as well. This effects not only Macbeth's nobles mentally, but also Macbeth himself. The nobles secretly hope that Malcolm will get help from England against Macbeth. Scotland is suffering mentally, emotionally, and physically from Macbeth's rule.