Firstly its normal for couples to argue, healthy even (it would be really weird if a couple that's been together for months to have never even had a mildly heated disagreement), and yes sometimes they get heated. However what matters most is the frequency and impact these arguments have on the relationship. If they are happening multiple times a week, and just as you get over the last one another one starts up again, or if all you seem to talk about is arguments you have then there is a problem. Some girls do get angry and that is also ok (and again quite normal), provided its never only as a result of what you have done or just targeted at you.
My girlfriend gets angry over tests, school stress and is just in a bit of a crotchety mood, easily annoyed by everything, everyone and anything and sometimes snaps at me. While I would prefer it if she didn't, she has never called me bad names, threatened me, upset me or not spoken to me for days, usually its just a case of not laughing at my jokes, getting pi55ed off when I ask her to repeat something, but she always says she is sorry afterwards and I can see she genuinely feels bad for it and thanks me for helping to calm her down eventually. Because I love her I don't mind.
Your case though... seems different. Your girlfriend seems to be taking all her anger out specifically on you. Threatening you, name calling and giving you the cold shoulder for days at a time is not healthy or normal. While my GF has never not spoken to me, I know some girls need a few hours to calm down, maybe a day, but not 5-6-7 days like yours does. A girl, hell, any person, you are in a relationship with, no matter how angry they are should never say they don't care about you. We all say things we don't mean in fits of anger, but not that. Manipulating and bossing you around is also not ok for what should be obvious reasons. You should leave her, the fact you are still with her makes me think she 'makes it up to you' by saying she loves you, but actions speak much louder than words. She seems to have no remorse after doing any of this, saying she is joking is actually even worse, and so you are better off without her.