Before I answer your questions (I assume that you are referring to Cubes - OLAP framework), I think it would be good to note, that Cubes has pluggable backends. Currently simple denormalisation-based SQL backend and MongoDB backend are implemented. I want to have them more advanced.
* Will data be fetched from the database for each query?
- currently yes, however we did some experiments with plain HTTP caching of Cubes/Slicer server and it worked pretty nicely for our current needs
* Is it possible to have dimensions with millions of values and expect reasonable query times?
- not tested yet
* Looks like it supports advanced topologies and hierarchies. How will dimensions with a high carnality affect performance?
- right, it supports hierarchies, however same as above: not tested yet for performance
I am open to any commeents/suggestions regarding the framework(s).
Stefan Urbanek, @Stiivi on Twitter (author of Cubes)