Op-amp gain bandwidth product
Gain-bandwidth product only has meaning w/r/t one op-amp: when you multiply the gain and bandwidth, you get a constant because of the way the op-amp is internally compensated.

When you have more than one stage, the overall gain times the overall bandwidth is not constant, so an overall gain-bandwidth product has no meaning. 

But your analysis of overall gain and overall bandwidth is correct, or at least mostly correct: it wouldn't be 500kHz, it would be slightly less. Bandwidth is usually measured in terms of a -3db point, so when you cascade two stages you get -6dB at 500kHz, and therefore the -3dB point is somewhere below that, probably in the 400-450kHz range.