But is specific heat capacity of water and latent heat of evaporation affected by pressure?

Not significantly, I don't think.

If you put boiling water at 100°C under a vacuum it will boil violently and water will go everywhere, so it's probably not a good experiment.

Suppose you depressurise it very slowly, so that the pressure is always just slightly below the equilibrium boiling pressure at the water temperature.

Now suppose you get to a temperature T after n moles of water have evaporated (of the original N moles). To evaporate a further dn moles requires latent heat of 44000*dn J. Assuming this heat must come from the remaining water, its temperature changes by dT, and this heat change is given by -75.3*(N-n)*dT J. From these expressions you can derive a differential equation for dT/dn, which shows how temperature changes with evaporation.

Can you now calculate the answer to question i?

Can you see from the equation that (with our assumptions) the answer to ii must be yes, however low a final temperature you choose, and the answer to iii is that it is impossible?