That's backwards. Light having different speeds in different media is what causes refraction when it encounters an interface at an angle. Note that light is not the fastest thing in a given medium. There is even a light equivalent to a 'sonic boom'.
Generally, what people mean by 'faster than light' is 'faster than 299,792,458 ms-1', the speed of light in a vacuum.
The mass of an object is given by the equation (iirc):
m = m0 / sqrt(1 - v2/c2)
i.e. if the rest mass is other than zero, the mass of an object moving at the speed of light will be infinite (this equation cannot be used to find any information about what happens when the rest mass is zero)
In any event, the bottom line is that faster-than-light travel is not "just an engineering challenge" in the same way that supersonic travel was. Even then, some engineering challenges aren't necessarily surmountable - for example, the Death Star's superlaser required about a thousand times more energy than its own estimated rest-mass converted into energy (and would have produced a much less spectacular bang).