NotSoRealMcCoy

Although I came across this situation in a city league softball game, I assume the rule would be the same across all leagues. Less than two outs, runner on third (or really any base), batter hits fly ball to an outfielder and the runner is tagging up. The fly ball hits the outfielder's glove and immediately pops up in the air a few feet, however the fielder then catches the ball on the way down before the ball hits the ground (so the batter is out). At which point can the runner tagging up legally leave the base; at the point the fielder first touched the ball or at the completion of the catch? A similar situation would be if after hitting the outfielder's glove, a second fielder actually ends catching the ball before it hits the ground (again, the batter is out). Does the runner have to wait until the ball is caught by the second fielder before leaving the base or can the runner leave when the ball initially touched the first fielder? And one last scenario: the batter lines a pitched ball that ricochets off the pitcher, causing the ball, never having touched the ground, to pop way up in the air, still in the infield. If a potential infield fly rule situation was in effect for this batter, could the IFR be applied here? I've asked several amateur umpires these questions and have received a medley of responses. Thanks.