(a) I get 406 m/sec so if its wrong we're both wrong. 1013mB is 101 325 Pa. rho 1.225 kg/m^3.
(b) Yes, concur, for supersonic flow the simple equation isn't really very useful.
Part of the issue may be that we don't really appreciate just how much force the atmosphere exerts. 14 psi or so is a lot. Do the maths on the force exerted on your house roof, if the house were a vacuum. You'd need some pretty impressive roof beams...