You're asking about underexposing one stop and then either push-processing by one stop to restore the density of the negative to normal, and thus printing at close to normal printer light numbers... versus developing normal and thus getting a thin negative and then using lower printer light numbers to compensate.
Either way you get more grain. Pushing increases contrast though and at higher printer light numbers, you get better blacks in the print (though as you push more heavily, you get an increase in base fog level.) Printing up a thinner negative, you get weaker blacks and thus it looks less contrasty.
You get a little color shifting with push-processing and some colors can look more intense.
Can't answer the second.



