Well water boils at 100 C and evaporates before it can get any warmer (with the exception of altitude/pressure). Therefore it cannot get any warmer.
Sure it can, you can heat the steam up. Note that when you say "water" you mean "liquid", when we say "water", we mean substance with a formula H
2O, whatever its state of matter is.
As risk of sounding like a complete goon I think it would be -40 C.
That's the only thing you got 100% right
Yes, water freezes at 0°C, but nothing stops it from getting colder.