The behavior of any substance changing between solid, liquid and vapor phases can be explained by the Phase Diagram. Here's a good "in general" one:
For water, you can go back and forth between solid (ice) and liquid (water) by melting and freezing, but only between certain temperatures and pressures (sorry - this chart doesn't have the pressure and temperature values shown).
You can go back and forth between liquid (water) and vapor (steam) by boiling and condensing, but once again, only within certain pressures and temperatures.
Finally, you can go between solid (ice) and vapor (steam) by sublimation and deposition, but once again, only within certain pressures and temperatures.
As for the cooling and freezing of water. Water freezes at 32 F at most pressures you are likely to run across. Let's say you have one pound of water at 40 F, and a second pound of water at 100 F. At these temperatures, the heat capacity (the amount of thermal energy required to change the temperature of one pound of water by one degree F) of water is relatively constant at 1 BTU/lb F. To get the water at 40 F to 32 F, you have to remove 40-32=8 BTU. To get the water at 100 F to 32 F you have to remove 100-32=68 BTU. This has to be done for both cups of water before you can start to talk about freezing them. Because the gradient (the temperature difference) between the 100 F water and your freezer temperature is greater than the gradient for the 40 F water and your freezer, the rate of heat transfer out of the 100 F water will be greater than out of the 40 F water. But it is not physically possible that the 100 F water will reach 32 F before the 40 F water reaches 32 F, in the same freezer.
Once water falls to 32 F it does not automatically freeze, any more than water automatically boils once it reaches 212 F. To get the water at 212 F to boil, you have to add an additional 1000 BTU/lb of thermal energy. I don't remember the exact value of heat you have to remove from water at 32 F to get it to freeze (not something I've ever used since school), but the value 472 BTU/lb sounds familiar.