When Faith told Buffy that she didn't care, I think it was more in the way a child would drop his eyes and say, "I don't care..." more as a defensive statement than as the truth. When she tried to convince Giles that it was Buffy who had actually killed the Assistant Mayor, it was, again, like a child's defensive, "She did it..." when being cought doing something wrong.
Primarily, Faith was, at the time of Seasons 3&4, a very immature young girl, probably feeling somewhat frightened and alone for the first time since her Watcher started taking care of her. She did quite a lot of growing up between Seasons 4&7, as illustrated in her ability to take charge when Angelus escaped on "Angel," and when she finally stood up to Buffy in Season 7, and when she at last tried to make ammends with the older Slayer in admitting her jealousy of Buffy's friends and family, things Faith herself had never really had.