In response to your pictures, if that spout serves the same purpose as the ones I see underneath 737's, then that's the waste water drain pipe. I'm not sure exactly what's connected to it in the T7, but definitely the lavs, and possibly the galleys? It reads "HOT" as it's heated during the flight to prevent ice from forming on it, and thus blocking the pipe.
Cool pictures though, wish I had access to airplanes like this one to take pictures of. KBFI's my local airport, but Boeing's rather skittish on letting people onto their ramps.