Check the chart I cited for the "triple point". For pressures at and below the triple point (4.58 torr from an old chemistry book), water will go from the solid state to the gasesous state or "sublimate".
To answer your question 1, No the speciman does not need to stay above 32deg F for the process to occur but, you have to go by the phase diagram again, at 32 and below you'll need stronger vacuum. As long as the vacuum/temp combo keeps you below that triple point and to the right of the solid line, it'll work.
We have chambers at work that are kept at room temp. Samples are frozen solid and put into the vacuum chamber. Once it's pulled down to the proper pressure it's solid...First time I saw it I was flabbergasted..I thought it would thaw...Heating will speed up the process though..
Don't forget about your condensation chamber,the freezer. The temperature will have to be cold enough for
deposition, i.e. gaseous phase to solid phase, to occur. You don't want the vacuum to be too strong or you'll pull all the water vapor through the pump...Pumps don't like water....

Luck,