Not really much to explain with an acetone wash. For MDMA I'd use about 15-20mL/g of cold anhydrous acetone or MEK. Stir up the product and tehn filter it, it should be much cleaner. I've seen GC results showing mid 90s for purity by the normal way or low 80s by the silly Dutch way. I prefer recrystallization myself. 50mL of acetone will dissolve a gram of MDMA when it's boiling. Slowly allow it to cool and collect the crystals by filtration and then let them dry to a constant weight, preferably in a desiccator. I would start with less MEK owing to it's much higher boiling point, but I don't recall the solubility offhand.
To make solvent anhydrous you can bake epsom salts in the oven (I do at least an hour at 400F, you'll see a change in the appearance when it's anhydrous vs some hydrate) then quickly crush them and add a lot them (I like to use about 1/4 of the volume of solvent) and shake thoroughly and decant the solvent. For polar solvents that form an azeotrope with water like light alcohols you'll probably want to do this 3 times, for polar solvents that don't like acetone you'll want to do it twice. If you really need to be certain that your nonpolar solvent is anhydrous once will probably do it, but that's not a common need at all. If you need to store an anhydrous solvent leave some of the anhydrous epsom salts in with it and really seal the bottle with something like electrical tape.