Evaluation of climate stability requires a stated time-frame under which that evaluation can be conducted. Since the end of the last glacial (or I could say since the beginning of this interglacial) the Earth's climate has been extraordinarily stable. Previous interglacial periods are slightly less stable than this one, and the glacial periods are considerably less stable than the interglacials (and there are good reasons for that).
Transitional periods are the most unstable periods of all.
But getting back to the original point, glaciers will advance or retreat in response to climate change. The more dramatic the change, the more pronounced the response.
Not according to the data, only after it has been minipulated to contracted recored history. The whole hockey stick theory is proven bunk. Besides, our planet's history is some 4,000,000,000 years old, if we finally stay relatively stable for 1,000 years (0.000025% of existance), does that prove our climate finally stabablized. I guess the first 99.999925% of our history as being unstable doesn't mean anything to you.