You don't have to sparge with hot water. Kai did an experiment comparing hot and cold sparge water (
http://braukaiser.com/blog/blog/2009/05/12/cold-water-sparging/), and found the efficiencies were the same within experimental error. You can also drain the wort as fast as your MLT will allow when
batch sparging. Once the sugar is fully dissolved in the wort, running off slower won't dissolve any more sugar as the wort and grains are in equilibrium. If your mash is long enough, the sugar will be in equilibrium. If you mash is not long enough, then you are not in equilibrium (and conversion may not be complete either), and in that case longer run off times can help more sugar dissolve.
A lot of the processes during the mash are controlled by diffusion: water into the grain, sugar and soluble starch out of the grain, etc. Smaller grain particles provide for shorter diffusion distances, so things happen faster. This can improve your conversion efficiency for a fixed mash time, and even allow a shorter mash with good conversion if the crush is fine enough. With very large particles, the diffusion processes may not complete before the end of the mash, in which case your efficiency will suffer.
Brew on