Does Niagara Falls ever stop flowing?
No, Niagara Falls never stops flowing completely. The water flow is reduced at night during the tourist season for hydroelectric power generation, but it never shuts off entirely. The Falls are fed by the Great Lakes, which have a massive natural flow, so you'll always see water going over the edge, even in winter when parts freeze.
The only time it "stopped" was in 1969, when the U.S. Army Corps of Engineers diverted the American Falls for a few months to study erosion. They built a temporary dam, and the American side was dry for about six months. But the Horseshoe Falls (the main Canadian side) kept flowing normally. That was a one-time engineering stunt, not a regular thing.
So, if you're worried about showing up and seeing a dry cliff, relax. You'll get your waterfall. Just don't expect a dramatic change in flow unless you're here at 10 PM when they throttle back for power—you'll barely notice the difference anyway.