At this age hitting, biting, pushing, pulling, and other aggression can be pretty commonplace amongst toddlers. Their frustration and anger is finding ways to get out, and they don't understand that hitting and pulling hair, etc, really hurts other people. Don't do it back, as this just teaches them that it's okay to do so when you're angry with someone. This type of punishment makes them lash out; instead, separate the children and explain why she was wrong - "Stacey is crying because you hurt her."
Another negative at this age is that toddler is learning how to lie. They've noticed that lying can get them out of trouble, and so will deploy it when they're worried or scared of the consequences of something. You must calmly explain that telling lies is wrong, and that she should be honest with you at all times. In return, be honest with her - don't promise rewards she won't get, and don't threaten punishments that you will not follow through.