4: "Where does he get those wonderful toys?"
In DC Comics canon, the Watchtower (the Second Watchtower to be precise) - the orbiting satellite/space station from which the Justice League. . . well, watches over Earth - is one of the many things made possible by Bruce Wayne's inexhaustible wealth. In the Marvel Cinematic Universe (and the comics) Nick Fury is director of S.H.I.E.L.D., head of operations of a global defense task force and commander of the Helicarrier - a floating fortress that guards us from super-human and extra-terrestrial threats. Seeing the similarity? Post Iron Man cameo, the role that Fury plays - especially in the Marvel Cinematic Universe is very much one of resource management and deployment. For that you need quite a lot of resources, and since the Justice League isn't exactly a government-funded covert operations outfit, they're going to need a backer. Someone to make sure that the Watchtower can be kept in orbit, can ensure access to Earth (either through Javelin jets or Transporter Beams), and keep first-class laboratories on the premises for scientist members like Ray Palmer. This gives Batman/Bruce Wayne additional responsibilities related to the League, making sure he always has a concrete reason to be hanging out with aliens, time-travelers, and demigods. It also gives Batman a reason to be familiar with all sorts of high-tech gadgetry/weaponry that could help him fight on equal footing with such superhero heavyweights as Superman and Green Lantern during the inevitable Act 3 showdown. The more you break it down, the more this sort of tactical/technical support role really suits Batman. As does an extension of that role...