Do we know what she was dying of?
I don't think we know. I can't find my fourth book, so perhaps Sirius or someone says that she was dying of a broken heart, if you believe that sort of thing. Maybe she always was in a fragile state of health for some reason or other, and her son's imprisonment sent her over the edge. Perhaps her poor health was something to do with centuries of pureblood inbreeding? You could probably make something up here.
Also do we know how old she was?
We don't know exactly how old. However, she was old enough to have a ninteen year old son, and a husband at the very top of the political ladder. That husband also out-lived her for thirteen odd years. Barty Crouch Snr could have lived a lot longer if it weren't for the whole Imperius Curse/being murdured thing. I think the youngest she could have been was thirty eight (this is assuming she became pregnant after she left Hogwarts rather than before), so I guess you could have her any age up from that.
And how long was she in Azkaban for before she died?
Not long. Barty Jr was in there for a year, but it was only when he was on his deathbed that his parents were allowed to visit and the switch was made. I don't think a time is specified, so it could have been anything from a few hours to a week, perhaps two. I don't think it would have been any longer than two weeks. My guess is about two or three days.
EDIT: Stupid Nargles. This is supposed to be the second post...
Wonderful avvie by psijupiter. Totally brilliant and amazing banner by Julia/the opaleye!