I think Attributes is a perfectly fine name for them - I knew exactly what you meant.
Dimensions don't have to be hierarchical, and very often aren't.
As to which aggregations it will store, there is no simple answer. It will depend on what DBMS you are using, and what you tell it to do. For example with SQL Server (SSAS) you can tell it to precalculate a given percentage of results, from 0 to 100. However within that you can't tell it which ones: it'll do that itself; you can only tell it e.g. 50%. I usually specify 100%.
Other DBMS's will have different facilities.