1. Earth to Sojourner. We've been terminating the thrust of solids on command since before I was born. It's critical for precisely targeted ballistic missiles. It's also trivially simple.
2. Range safeties require the ability to be built in to any really large solid.
1. Not any more. They use a trajectory optimization maneuvers to use up all the impulse of the motor so that thrust termination systems would not be needed because they were not trivially simple. Or They use liquid in the final stage.
2. It is thrust termination by destruction. They split the whole casing lengthwise.
You don't know what all the impulse of the motor is until it's too late to do anything about the error, because once you've found out how big the error is, the motor has quit burning. It's a catch-22. The IUS on the Shuttle does use trajectory optimization, with each flight planned with months of simulations to make sure a satellites own RCS fuel won't be overly consumed to correct a residual error due to the inexact final impulse (which is accurate to about 0.5%)
The Polaris, Minuteman, and other missiles have ports on the forward dome that operate explosively within about 2 milliseconds, providing a net negative thrust for re-entry vehicle seperation, while not directly impinging on the subsequent stage. Lockheed, UTC, and Aerojet were involved in the design, as I recall, and the knowledge that you could precisely terminate a solid's thrust like that was a high-classified secret for a long time, eventually leaking out because we used the same boosters for space flight. The Russians adopted the same system, and our ABM systems have to distinguish between the re-entry vehicle, staging parts (bolts, washers), and warm pieces of fuel blown through the forward thurst termination ports that tend to travel along near the RV, giving off their own infrared signatures.
The Shuttle SRB's thrust termination system comes from the Minuteman research, and sounds very similar, consisting of six shaped charges in the upper dome of the casing. The systems on both engines are tied together, so if the system on one engine is fired the system on the other engine is also fired automatically.