Hale came to Salem feeling quite confident in his abilities to root out the Devil and force him to let go of good Christians. But as time passes, he becomes less and less confident about everything he knows as well as the motives of some of the accusers; however, in Act Two, at least, he still believes in the court's ability to suss out the truth. At John Proctor's house, when Francis Nurse tells Hale that his wife has been charged with murdering Goody Putnam's babies, Hale is said to be "deeply troubled." He "plead[s]" with Nurse to allow the courts to do their job as he still feels that "the Devil is alive in Salem." However, he does feel "great pain" as he tells Nurse and Giles Corey to "remember [that] until an hour before the Devil fell, God thought him beautiful in Heaven."
Hale tests John and Elizabeth Proctor because they have not been to church often of late—only twenty six times in seventeen months—and because her name was mentioned in the court today. John tells him that Elizabeth has been ill for some months and that this is the reason they haven't been to church. However, there was also the rumor Reverend Parris approached Abigail with in Act One: that Elizabeth doesn't come to church because she "will not sit so close to something soiled." This is, of course, a possibility as well. It must be painful for Elizabeth to be in Abigail's presence knowing what happened between Abigail and John.
Hale realizes the evil nature the court has taken. Originally, Hale thought it would expel Satan from Salem, but he comes to realize that something far worse is there: lies and vengeance. Once he realizes that the girls are lying and that there never was any real evidence of witch craft, he removes himself from the court. He tests Proctor and Elizabeth because at that time he was still an agent of the court. It was his job to make sure they were good and upstanding Puritans and that the charges against Elizabeth were unfounded. Proctor refuses to go to church mainly because of his dislike for Rev Parris. Proctor believes Parris is a greedy person. Note how Proctor tells Hale how Parris kept asking the congregation for golden candle sticks. Also Parris focuses very little of his sermons, again according to Proctor, on God, focusing instead of hell and damnation.
Many questions! I'll take the first one. Hale has been recognized as an authority figure in town. He is accepted as the leader, and as the deciding factor in the guilt and innocence of the accused townspeople. However, he has begun to realize that all is not what it seems or what he assumed. He has started to suspect that the accusations may not be all that they seem.