1) "Non-polar vs polar" is kind of synonomous with "organic vs water". Calling something "organic" in this context is the same thing as calling it non-polar or is another way of saying that it is much less polar than water. So you could call acetone either an organic solvent or a non-polar solvent. There is a little bit of nuance to the meanings, but for these purposes, they are the same thing. Polar vs non-polar is also a sliding scale, not an on/off switch. Acetone is much less polar than water, but much more polar than hexane.
In terms of polarity: water > acetone > hexane (and there are dozens of other solvents with varying positions on the scale)
Then, to further complicate it:
water and acetone mix to make a homogenous solution
hexane and acetone also mix to make a homogenous solution
BUT
water and hexane do not mix
2) MDMA that has not been made into a salt is non-polar and would thus be soluble in acetone and other more non-polar solvents. But since what people always have is the salt of the amine, it is now an ionic compound. Ionic compounds are generally only soluble in more polar solvents, like water. So when you do a dry acetone wash, leftover reactants, side-products, etc, anything like that from the synthesis are dissolved and wash through the filter. The MDMA salt is insoluble in the acetone, so it stays behind on the filter.
The issue that futura brought up about it only cleaning the outside of the crystals is true, however, the effects of this are very minor, as the crystals are usually very small. Unless you have "moon rocks", the crystals are probably very small and powdery, in which case this will clean them up just fine. If you have large chunks and you want to clean them, you should either crush them up in some way first, or crush them up while they are in the acetone.