Obviously, the true answer is that I have no idea, but if by multiple universes you are referring to the many-worlds interpretation of Quantum Mechanics, it might depend on which Universe you are referring to.
In the many-worlds interpretation, all possible events do indeed occur, but in separate parallel universes. In this case the properties of a particular "universe" compared to our own would likely depend on the point at which it diverged and its subsequent evolution. The vast majority of these universes would be incredibly similar to ours, since as Statistical Mechanics indicates, our own universe tends to progress along the "most probable path". This means our reality unfolds along the path that is virtually identical (at least on a macroscopic scale) to the most other possible paths. However, in this case there should be a mind-numbingly small number of universes that actually do not follow the most probable path. What this means is that at least for some period these alternate universes would violate the 2nd law of thermodynamics.
As for other physical laws and constants, I would guess that while the vast majority of parallel universes that have diverged recently from our own would have identical physical laws and constants, it is possible that some universes that diverged near the very beginning of the Big Bang (or essentially at the beginning), would have evolved along paths leading to alternate physical laws and constants. Of course none of this is really understood, especially by me, so I could be completely wrong.