Please can you give a character analysis of Danforth in The Crucible.Act 3.
You have asked two questions, which is against enotes regulations, so I have cut it down to one question. In answering your question, I think we need to remember the position that Danforth had - he was Deputy Governor, who is introduced in the following way in the stage directions by Miller:
On his appearance, silence falls. Danforth is a grave man in his sixties, of some humour and sophistication that does not, however, interfere with an exact loyalty to his position and his cause.
Thus he is introduced as a man who is strictly loyal to what he believes is important and the truth, wherever that will take him and whatever he will need to do to be true to that position. It is his position and his belief in the justness of his actions that give him the incredible arrogance that we see in Act Three - he ignores the pleas of Giles Corey and Francis Nurse, who are desperately trying to save their wives by reference to the authority of the court:
This is the highest court of the supreme government of this province, do you know it?
Of course, a man such as Danforth will not take kindly to being challenged by farmers, when "seventy-two [are] condemned to hang" on his signature. We are presented, then, with a man who is so sure of himself and his position and the righteousness of his cause, that he will not be persuaded to accept or see any other view point - it is this divine task that he feels he has been given that leads him to act in the way he does. Consider the following quote:
...a person is either with this court or he must be counted against it, there be no road between. This is a sharp time, now, a precise time - we live no longer in the dusky afternoon when evil mixed itself with good and befuddled the world. Now, by God's grace, the shining sun is up, and them that fear not light will surely praise it.
This perhaps explains Danforth's position completely - there are two sides in this play - the side of the court and the side of the Devil, and Danforth feels it is his job to discern where everybody belongs and to punish them accordingly.