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The symptoms in your child are not listening to others, not obeying commands, bullying attitude, projecting mistakes on others, habit of stealing etc should not be taken as normal.
They are definitely due to some disorder. Most likely she might be having Oppositional Defiant Disorder
(ODD). In this disorder children don't follow commands, show criminal behavior, fights with others, have defying attitude, tells lie etc.
Other possibility may be some Childhood Bipolar Disorder
, in which such symptoms are seen but mood symptoms are also seen.
I would advise you to take her to some good Psychiatrist
as this behavior is not normal, and proper treatment at earlier stage of disorder will slow down the progression.
Dr. Seikhoo Bishnoi, MD