@Jonas Dahl
Q: Can I store my cached simulations and switch between different caches?
A: In 2024.4 you can now cache all simulations as external files (alembic). You don't get the nice list UI to conveniently switch between caches, but there is a parameter called "path to Alembic File" which you can change to different versions.
Q: Can I keyframe / move positions of several caches in the Timeline after caching them?
A: You can offset the whole animation using the Offset parameter in the cache tab. If you need it in the timeline you can turn off "Use Animation" and create keys on the frame parameter. That allows you to both offset and retime your cache. For simple time remapping there is also a spline UI.
Q: How can achieve caching only a few frames instead of the whole timeline?
A: There is an "enable" parameter in the basic tab of each simulation tag. You can use that to control on which frame the simulation starts and what is being cached. If you want the simulation to start at an earlier point in time but only cache a subset, I think the only way is to use the alembic exporter directly to set a specific start and end frame.
Q: If I disable an object with a simulation tag in the viewport and render, the simulation is still being calculated, right?
A: I believe that's a bug.