I too thought it was pretty cool when I first saw it, but frankly I've never found a use for it in real code, so I'm not sure how useful it actually is.
There's no equivalent in C#.
You don't get a DivideByZeroException because you're using the floating point division operator (/) and not the integer division one (\). Only integer division by zero throws, floating point generates NAN or infinity or something like that.
0/0 is NaN (Not a Number). If x>0, then x/0 is Infinity ; if x<0, then x/0 is -Infinity. It's defined in the rules of IEEE (some number which I definitely don't know off the top of my head) floating point numbers somewhere.
Incidentally, you can definitely get the same behavior in C#, as per...