Do food trucks have running water?
Yes. A food truck that prepares food carries its own running water: a fresh water tank, a pump to pressurize it, a water heater and a wastewater tank. The FDA Food Code requires water under pressure at every fixture that needs it, and Texas requires hot and cold water under pressure at all sinks.
Gravity-fed jugs usually won't pass. Oregon requires at least 20 PSI at all sinks and doesn't allow gravity feed. Tanks are filled from an approved source with a food-grade hose, through an inlet no wider than 3/4 inch under the Food Code.
Wastewater goes out at the commissary or an approved dump site. King County, Washington says never on the street or the ground. See food truck sink requirements and the commissary entry.