If you take any finish and put it into a jar and watch it over days the finish will settle to the bottom and the solvents come to the top. By pouring off the top of your shellac solution you will be getting mostly alcohol and then throw the finish away. It's why every time a finish is used it should be thoroughly stirred or agitated.
I can't tell you specifically but there is a method of filtering the wax out of shellac. This is how Sealcoat is made. You might do some homework and find out what is necessary in the forms of filters. Unless you plan to topcoat the shellac with polyurethane I don't see the need to worry about the wax. It's just a natural part of the finish and more than likely the finish would last longer with the wax than without it.
Not exactly. Essentially, the wax is settling because it is less solvable in the solvent. It's essentially a precipitation extraction. This is in fact how they dewax the shellac; however, instead of letting it sit, they pass it through a filter. Since the wax forms a precipitate, the wax gets caught in the filter. The rest of the resin remains dissolved and as a result, passes freely through the filter.
However, it could depend on the solvent and the temperature. If the solvent does not dissolve the rest of the resin sufficiently, one could imagine some of it settling with the wax. However, DNA and 95% ethanol both are more than sufficient at dissolving the resin. In fact, some extraction processes use a rather poor solvent, but heat the solution up to a point where the resin's solubility is sufficient, but the wax still crashes out.
If anyone is worried, just simply weigh your dewaxed shellac in a jar and add their favorite solvent. Then, after settling occurs, come back and decant the solution (supernatant), let what has settled in the bottom dry out, and then weigh again. With this, you will be able to calculate how much of your solids have been removed by this process. I doubt you will find that most of the solids will have precipitated from the supernatant. I would also wonder how much of the precipitate is just more wax that was then purified out again by a second run.