Does “stupidity” and “courage” affect the performance of kerbonauts

The Stack Separator decouples from both the child and the parent node whilst the Stack Decoupler remains attached to the child.

Why might I use one over the other?

Situations where you are separating satellites, rovers, probes or other payloads and don't want the Decoupler still attached.

Currently (0.23), there is few practical difference between sandbox and career mode after you unlocked the whole tech tree. You have all parts available and are free to use them to do whatever you like.

The only difference is that you can still use experiments in career mode, while in sandbox mode all experiments are disabled. This doesn't give you any gameplay benefit, but it gives you the opportunity to read the flavor texts of the experiments performed on outer planets and moons. Some of them are quite interesting and/or entertaining. One EVA report on Eeloo is really cute, by the way.

Currently there is a lot more science to farm in the KSP solar system than you need to unlock the whole tech tree. And considering that it is planned that more planets than just Kerbin, Mun and Minmus will gain different biomes, the science output will just increase. If and how the developers will balance this in future updates (more tech tiers? Make later tiers more expensive? Scale down scientific values? New uses for science points?) is currently just guessing.