If you can throw a 90 MPH fast ball stationary I assure you that it will exceed 90 MPH if you throw it from a moving vehicle, same thing with the explosives.

I'm almost 99% sure a incoming warhead speed wouldn't be even close to 8000 m/s. The space shuttle doesn't even fly that when in orbit with no atmospheric resistance.

The direction of the missile travel is constantly corrected based on the incoming trajectory....im pretty sure if a nuke was on its way there would be quite a few Pats in the air, it would get hit. Laser technology is used and is very effective but its still in its baby stages.