Reading through your letter, it sounds like your loved one has had a tough road over the past several months. In my 15 years of experience as a nurse, I
see many people end up in this kind of situation as they near the end of their life. Many chronic health problems start to take their toll on a person, like your loved one. They may get through each crisis (hospitalization), but each time the come home they are a little weaker, a little less able to care for themselves. Now, she is in a situation where she cannot take care of herself at all. Her quality of life is poor, and she has been in the hospital, which can be exhausting and scary, far too many times.
Now, on top of her CHF and kidney failure, she has gangrene. You do not say what kind of gangrene she has (there are 3 kinds: dry, wet, and gas). I am going to assume it is dry gangrene because her circulation is poor. Since she will not have surgery, she will eventually get a fatal infection in her legs that will end her life. I am sure her doctors have told her this, but I think that she is making a choice now to stop many of these invasive medical treatments. I think that she is reaching a point where she has had enough, and that is OK. I do understand her hesitation with dialysis, as it is hard for many people to do, and I can really understand why many people choose not to do at all, or to stop it. It really impacts quality of life, and it can really make you feel tired on the days it gets done. Regarding the offer of surgical amputation of her legs, with her heart problems, the chances of her surviving a leg amputation are slim at best. She has reached the point in her life where the options she has will not really extend her life much more.
You ask how long she can survive. In reality, she probably has months to live, and if she does not go back to dialysis, her prognosis may even be less than that. I would suggest she consider hospice now, as it seems more in line with her wishes. I know that many people have this idea that hospice means that you are giving up, but this is not the case. Hospice means that the focus of someone's care has changed from trying to cure medical problems at all costs to taking care of her problems in a way that makes her comfortable.
I personally know that it is hard and truly painful to let someone you love go. But, it is her life, and her choice to make. The best thing that you can do is to be supportive of her decisions, and enjoy her for the time you have left together. I wish you luck.