>>64497572 (OP)
>How would it protect itself from long range missiles?
With DEWs of course? It's got a nuclear reactor, power isn't an issue, and lasers are very effective at altitude with extremely long LOS, thin atmosphere, and no clouds in the way. Probably auto turrets and micromissiles would be good tertiary defense as well just in case, but AAMs are going to lose to powerful lasers pretty badly.
Though I think if anyone was doing a serious capital nuclear air fleet you'd actually want more then just the stratocarrier, as with a surface fleet you'd probably want the big carrier and then a few nuclear escort aircraft focused even more heavily on anti-air and maybe some level of powerful anti-ground/ECM as well.