Explain why Mary Warren thinks Elizabeth should speak civily to her in The Crucible?
I think Mary Warren's assertion that Elizabeth should speak civily performs two additional functions:
1. It serves as a threat. Mary is understanding her new found power as one of the girls helping identify those possessed by the Devil. It seems to me that Mary might be suggesting that it might be difficult for her to make decisions between doing the right thing and proving loyal if Elizabeth Proctor's name should ever arise.
2. It foreshadows what is to come. Mary Warren will turn on Elizabeth, if you haven't seen her do it already. Although Proctor is going to make every effort to help Mary do the right thing, she won't. She will use her advantage with the court not necessarily for her own power, but because she is a weak conformist.
In Act II, Mary Warren does not like the way that Elizabeth Proctor is speaking to her. She feels that she deserves more respect now that she is connected to the court that is investigating the allegations of witchcraft.
Before this, Mary has simply been a servant working for Elizabeth Proctor. As such, there is no reason that Elizabeth has to be particularly respectful to her (especially in those days). But now Mary is connected to the court and she feels that she is more important and deserves respect.
Because of this power, Mary sort of threatens Elizabeth as well. She points out that Elizabeth has been accused but that Mary's testimony saved her. This implies that if she makes Mary mad, Mary turn against her.