Here is an explanation. The reason they Barge in and tell her they want her to return to the Dursleys is to use her as a scapegoat if something goes wrong they can blame it on her. Saying that the reason that she is there is because she is nothing more than a squib. They have no power over her there at the lair. They traced her to the lair using the Trace. Harry is acting out of character because in here he is a spoiled brat who always gets what he wants and has let the fame get to his head. In here he is NOT the chosen one.
There is a meaning behind her looks
Her hair is scarlet red. I found this fitting since she has a temper and can be reckless. Her eyes are bold and bright. Like her personality and mind. The tattoos are used to cover up markings. Ones that will later be discovered.
Why is she a mutant and why can she shift?
To show that even those who suffer can fit in to a point. Her cat like reflexes and her front and back help her fight. She was mutated by a figure soon to be revealed.