In The Crucible by Arthur Miller, what are some examples of indirect Puritan characterization?
You asked more than one question so I have had to edit your question down. Please remember that you can only ask one question.
You have asked a very interesting question that explores the Puritanism of the play and the way in which some of the characters are so focussed on their particular brand of religion that they are not able to look outside of that and discover the more sensible and logical explanations for what they are witnessing.
In a sense, this is linked to a key theme of the play which is bigotry. Throughout the events in Salem we see the effects of religious zeal, fear of heresy, intolerance and superstition. Reverend Hale, for example, is so proud of his knowledge of witchcraft that he is quick to accept the girls' confessions as proof of this skill. Others are more than willing to accept supernatural reasons or "unnatural causes" for their problems. There appears to be so much insecurity in the young colony that anyone who questions the authorities, either religious or state, is seen to be launching an attack on the whole foundations of society.
The character that to my mind models this kind of un-thinking Puritan bigotry the best is Danforth. Consider how he talks to Giles Corey, Francis Nurse and John Proctor in Act III:
But you must understand, sir, that a person is either with this court or he must be counted against it, there be no road between.
Sounds rather like George Bush to me! But also, it presents us with a character who is so completely assured that he speaks the truth and the way that he looks at the world is the correct one - no matter what evidence presents itself.