Drying organics at high temp is rarely a good idea. It can lead to oxidation or other degredation pathways. The best way is usually to pull vacuum on the material and let it sit overnight. Sometimes gentle heating is required depending on the power of the vacuum and the solvent's boiling point.
Acid/base extraction will only work for removing acids or bases from non-ionizable compounds. This means you could use it to remove your di-ester (non-ionizable) from the di-acid and mono-ester (both can donate protons to form anions).
MeCO2-Ph-CO2Me + base
no reaction, soluble in organic solvent
MeCO2-Ph-CO2H + base
MeCO2-Ph-CO2
- + BH
+, soluble in water
Same general reaction for di-acid.
You can also use this technique to separate sulfonated product from unsulfonated product, as long as the unsulfonated product is incapable of ionizing.
Another wrinkle is that your sulfonic acids (what you are ultimately trying to make) tend to be very strong acids. This will probably result in the product being very water soluble. Write out all of the possible charged states of your target compound and suspected byproducts and at what pH they should be charged or uncharged before attempting any sort of acid/base extractions. I would consult a pKa table for this.
As for cleaning up the p-xylene sulphonic acid oxidation: the reference should have described how they purified their material. I would keep following the procedure.
The orange stuff in the reaction? Who knows!? Frequently during organic reactions colored byproducts are formed. For some reason they almost always tend to be somewhere in the yellow, red, brown range. Frequently its a small amount of material with a huge extinction coefficient so a tiny bit causes a dramatic change in color. Sometimes they can be removed by extraction; activated charcoal is an older method of removing colored impurities, and chromatography can also frequently be used to remove these impurities.