Pressure causing water to boil at a lower temperature

Hi , I have a bit of a science question that I would really appreciate an answer or even a good place to research further. Unfortunately my Year 7 science education isn't enough to cover this one!

Context: My friend was telling me that water actually boils at different temperatures based on the pressure it is exposed to. If the pressure is low enough, water will boil at room temperature! I vaguely remember knowing this but when I read further, also found another interesting fact: As the water boils, it gets colder because the hotter molecules are the ones first to boil out and get sucked up by the vacuum decreasing the pressure.

Questions:
- Is this true? Does water get colder as it boils if you applied some sort of vacuum suction to it or is there another mechanism? (Explain like I'm 5 please!)
- How long would it take before we could chill it to 0C? I presume at this temperature, if we suddenly exposed it to room pressure then it would phase change straight back to ice?
- Is there a table or equation that can explain this decrease in temperature? I.e Is there some way that we can calculate at what rate the temperature of water decreases for given rates of pressure decrease?

Thanks!
Sophie