Chemical water treatment: Acid Base reaction
The question is long and detailed, and deserves a long answer, but I can only hit on the highlights, and urge others with some expertise in this area (which I lack) to weigh in.

First, the science of water treatment is mature and has addressed many of the issues raised here, primarily through biological and chemical processes which are very good at breaking down and dissolving most of the different sized particles you refer to. 

As far as the composition of sewage is concerned it contains a lot more water than human waste, and a lot more normal waste (urine and fecal matter) than vomit, which, since most people are sick only a tiny fraction of their lives, and nauseous an even smaller fraction, likely is a vanishingly small contributor to the content of sewage. The composition of sewage at the treatment plant intake varies much less, and more slowly, than you might think, since it is averaging the inputs from people all over a city or region. Still, it may vary seasonally due to changes in temperature or water usage, so the treatment must vary accordingly, as you have surmised.

Finally, you concern about neutralizing every last iota of HCl is misplaced. Adjustment of pH is commonly used in sewage treatment and is done using automated equipment and pH sensors that can withstand extended exposure to sewage and to pH fluctuations. The glass membrane electrode is a workhorse that is stable to extremes of pH well beyond what would occur in sewage.

But I conclude my answer by saying that some of your ideas are very interesting, and there may be many applications of nanotechnology in water treatment along the lines you mentioned, that could have practical benefits for peoples' lives. I urge you to continue your studies of wastewater chemistry with your full vigor and an open mind.