What is indicated when a flaming splint causes a pop?
This means that in the chemical reaction that occured, hydrogen (H2) gas was produced. The splint will make the popping noise because literally there is a small explosion occuring, and water vapor will form.
Lots of ways. Density and spectroscopy come to mind, but if you're just looking for a quick test of a small quantity and you don't mind using it up in the process: A smoldering (not flaming) wooden splint inserted in a test tube of oxygen will flare into life. A flaming splint inserted in a test tube of hydrogen will cause a small "pop" (and probably blow the splint out) as the hydrogen combusts.