We have a pull request for partitioned hash aggregations, but currently all the groups must fit in memory limit specified by the "task.max-memory" configuration parameter (see http://prestodb.io/docs/current/installation/deployment.html for details).
Regarding approximate queries, we are working with the author of BlinkDB (http://blinkdb.org/) to add it to Presto. BlinkDB allows very fast approximate queries with bounded errors (an important requirement for statisticians / data scientists).
2) Presto is a traditional SQL engine, so it would be ROLAP. We don't yet have any support for building cubes or other specialized structures (though full materialized view support with rewrite is on the roadmap).
The Presto query engine is actually agnostic to the data source. Data is queried via pluggable connectors. We don't currently have any caching ready for production.
There is a very alpha quality native store that we plan to use soon for query acceleration. The idea is you create a materialized view against a Hive table which loads the data into the native store. The view then gets used transparently when you query the Hive table, so the user doesn't have to rewrite their queries or even know about it. All they see is that their query is 100x faster. (All this code is there today in the open source release but needs work to productionize it.)
We have a dashboard system at Facebook that uses Presto. For large tables, users typically setup pipelines in Hive that run daily to compute summary tables, then write the dashboard queries against these summary tables. In the future, we would like to be able to handle all of this within Presto as materialized views.
3) We're excited about the Drill project. They have some interesting ideas about integrating unstructured data processing (like arbitrary JSON documents) with standard SQL. However, last I looked they were still in early development, whereas Presto is in production at Facebook and is usable today. Please also see this comment: https://news.ycombinator.com/item?id=6684785