How do I deal with my visa sponsored partner who doesn't love me but threatens to harm herself if I don't sign the residency forms?

Why are you still with a who doesn’t love you. I recommend that if you are living with her that you either move out or find her a place to live (such as a woman’s shelter). Do not sign the residency form for any reason whatsoever. It is very apparent that she is just trying to manipulate and once she gets those form signed she won't care diddly-squat about you, which she does not appear to care anyway. It is not your fault if she commits suicides or harms herself. However, if you really think there is a possibility of her harming herself call the National Suicide Prevention Lifeline at 1-800-273-8255 and ask for help, or call authorities or some other place like that.