There's definitely some physical underpinnings--most music systems have the concept of an octave which maps nicely onto frequency-doubling, for example. But there's also culture: For a purely Western example, even-tempering is in tune, but you'll hear different "beat patterns" for a given interval than with an instrument tuned for music in just one key.
No it isn't. You can hear integer pitch ratios in the same way you can see, e.g., the difference between a square and a rectangle or between a circle and an oval.
But more than 90% of all the written-composed music from western Europe and North America (at minimum) over the last several centuries does not use integer pitch ratios.