MongoDB does have very good support for Aggregation kind of functions. There are no joins of-course. The way MongoDB Schema is usually designed is such that you would typically not need a join.
HiveQL operates on 'Tables' in HDFS. That's the default behavior. But you have a MongoDB-Hadoop Connector: http://docs.mongodb.org/ecosystem/tools/hadoop/ which will let you query MongoDB data from within Hadoop.
To use Map Reduce you can do that with MongoDB itself (without Hadoop). See this: http://docs.mongodb.org/manual/core/map-reduce/