It's hard to find characters that AREN'T in the middle of some sort of conflict in this play, especially in Act Three. This is a very intense act where many people are condemned and arrested, and where the illogical and infuriating courts refuse to see any reason to stop the chaos that is occurring. Here's a list of some characters, and their conflicts:
1. John Proctor. His wife has been arrested, and he wants to free her. He is faced with the fact that people who signed his petition are now arrested, his friend has been arrested for trying to prove Putnam a manipulating murderer, and now he has to try to prove that Abby and the girls are frauds. It is hard to do this without confessing Abby's sinful nature (and exposing himself as an adulterer), so he is relying on the cowardly Mary Warren to come through. When she doesn't, he is presented with the conflict of whether to reveal Abby as a whore; he does, then is presented with the conflict of whether or not to confess to witchcraft as Mary turns on him.
2. Mary Warren is faced with the conflict of telling the truth and facing the potential wrath and false accusations of Abby and her clan, or to cower out and go back to Abby and the farce in order to save her own skin. She backs down in the end, and betrays the truth and John Proctor.
3. Elizabeth Proctor is faced with the conflict of lying to save her husband's reputation, or telling the truth about the affair and ruining her husband's reputation.
4. Abby is faced with the conflict of John and others dragging her own reputation through the mud, and the fear that she will be exposed as a fraud and a loose woman. She takes that conflict head on by denying any wrongdoing, and then turning on Mary as a distraction, and a bullying technique.
5. Giles Corey is faced with the conflict of giving up his witness's name and save his own skin, or keep the witness's name and be arrested. He takes the brave route and keeps it a secret.
Those are just a few key characters that deal with conflict in this act, and how each of them responds are good indicators of the integrity (or lack thereof) of their characters. I hope that helped; good luck!